BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Per von Soosten (Harvard University) DTSTART:20200427T201500Z DTEND:20200427T211500Z DTSTAMP:20260404T094122Z UID:Probability/1 DESCRIPTION:Title: Localization and delocalization for ultrametric random matrices \nby Per von Soosten (Harvard University) as part of MIT probability s eminar\n\n\nAbstract\nWe consider a Dyson-hierarchical analogue of power-l aw random band matrices with Gaussian entries. The model can be constructe d recursively by alternating between averaging independent copies of the m atrix and running Dyson Brownian motion. We use this to map out the locali zed regime and a large part of the delocalized regime in terms of local st atistics and eigenfunction decay. Our method extends to a part of the delo calized regime in which the model has a well-defined infinite-volume limit with Holder-continuous spectral measures. This talk is based on joint wor k with Simone Warzel.\n LOCATION:https://stable.researchseminars.org/talk/Probability/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Amol Aggarwal (Harvard University) DTSTART:20200504T201500Z DTEND:20200504T211500Z DTSTAMP:20260404T094122Z UID:Probability/2 DESCRIPTION:Title: Pure States in the Ferroelectric Six-Vertex Model\nby Amol Aggarwal (Harvard University) as part of MIT probability seminar\n\n\nAbst ract\nThe classification and analysis of pure states (translation-invarian t\, ergodic Gibbs measures) for statistical mechanical systems is a fundam ental question in mathematical physics. In this talk we investigate this q uestion for the six-vertex model in its ferroelectric phase. We will see t hat the situation here differs considerably from its more well-known count erpart for dimer models. In particular\, for the ferroelectric six-vertex model there now exist non-trivial regions of non-existence and new familie s of highly anisotropic pure states exhibiting Kardar-Parisi-Zhang (KPZ) f luctuations.\n LOCATION:https://stable.researchseminars.org/talk/Probability/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Marianna Russkikh (MIT) DTSTART:20200511T201500Z DTEND:20200511T211500Z DTSTAMP:20260404T094122Z UID:Probability/3 DESCRIPTION:Title: Dimers and embeddings\nby Marianna Russkikh (MIT) as part o f MIT probability seminar\n\n\nAbstract\nOne of the main questions in the context of the universality and conformal invariance of a critical 2D latt ice model is to find an embedding which geometrically encodes the weights of the model and that admits "nice" discretizations of Laplace and Cauchy- Riemann operators. We establish a correspondence between dimer models on a bipartite graph and circle patterns with the combinatorics of that graph. We describe how to construct a '$t$-embedding' (or a circle pattern) of a dimer planar graph using its Kasteleyn weights\, and develop a relevant t heory of discrete holomorphic functions on $t$-embeddings\; this theory un ifies Kenyon's holomorphic functions on $T$-graphs and $s$-holomorphic fun ctions coming from the Ising model. We discuss a concept of 'perfect $t$-e mbeddings' of weighted bipartite planar graphs. We believe that these embe ddings always exist and that they are good candidates to recover the compl ex structure of big bipartite planar graphs carrying a dimer model. Based on: joint work with R. Kenyon\, W. Lam\, S. Ramassamy\; and joint work wit h D. Chelkak\, B. Laslier.\n LOCATION:https://stable.researchseminars.org/talk/Probability/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Eitan Bachmat (Ben-Gurion University) DTSTART:20200921T201500Z DTEND:20200921T211500Z DTSTAMP:20260404T094122Z UID:Probability/4 DESCRIPTION:Title: On maximal (weight) increasing subsequences\nby Eitan Bachm at (Ben-Gurion University) as part of MIT probability seminar\n\n\nAbstrac t\nWe will discuss the connection between the first order asymptotics of m aximal weight increasing subsequences and comparison of natural (and imple mented) airplane boarding policies.\n\nWe then consider the behavior of we ight fluctuations of maximal weight increasing subsequences by viewing the m as discrete versions of maximal proper time curves in various space-time domains.\n LOCATION:https://stable.researchseminars.org/talk/Probability/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Rhodes (Aix-Marseille Université) DTSTART:20200928T201500Z DTEND:20200928T211500Z DTSTAMP:20260404T094122Z UID:Probability/5 DESCRIPTION:Title: Conformal Bootstrap in Liouville theory.\nby Remi Rhodes (A ix-Marseille Université) as part of MIT probability seminar\n\n\nAbstract \nLiouville conformal field theory (denoted LCFT) is a 2-dimensional confo rmal field theory depending on a real-valued parameter γ and studied sinc e the eighties in theoretical physics. In the case of the theory on the Ri emann sphere\, physicists proposed closed formulae for the n-point correla tion functions using symmetries and representation theory\, called the DOZ Z formula (when n=3) and the conformal bootstrap (for n>3). A probabilisti c construction of LCFT was recently proposed by David-Kupiainen-Rhodes-Var gas for γ in the half-open interval (0\,2] and the last three authors lat er proved the DOZZ formula. In this talk I will present a proof of equival ence between the probabilistic and the bootstrap construction (proposed in physics) for the n point correlation functions with n greater or equal to 4\, valid for γ in the open interval (0\, √2). Our proof combines the analysis of a natural semi-group\, tools from scattering theory and the us e of Virasoro algebra in the context of the probabilistic approach (the so -called conformal Ward identities).\n LOCATION:https://stable.researchseminars.org/talk/Probability/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacapo Borga (Universität Zürich) DTSTART:20201005T201500Z DTEND:20201005T211500Z DTSTAMP:20260404T094122Z UID:Probability/6 DESCRIPTION:Title: Scaling and local limits of Baxter permutations and bipolar ori entations through coalescent-walk processes\nby Jacapo Borga (Universi tät Zürich) as part of MIT probability seminar\n\n\nAbstract\nBaxter per mutations\, plane bipolar orientations\, and a specific family of walks in the non-negative quadrant\, called tandem walks\, are well-known to be re lated to each other through several bijections. In order to study their sc aling and local limits\, we introduce a further new family of discrete obj ects\, called coalescent-walk processes and we relate them with the other previously mentioned families introducing some new bijections.\n\nWe prove joint Benjamini-Schramm convergence (both in the annealed and quenched se nse) for uniform objects in the four families. Furthermore\, we explicitly construct a new random measure of the unit square\, called the Baxter per muton\, and we show that it is the scaling limit (in the permuton sense) o f uniform Baxter permutations. We further relate the limiting objects of t he four families to each other\, both in the local and scaling limit case. \n\nTo prove the scaling limit result\, we show that the associated random coalescent-walk process converges in distribution to the coalescing flow of a perturbed version of the Tanaka stochastic differential equation. Thi s result has connections with the results of Gwynne\, Holden\, Sun (2016) on scaling limits (in the Peanosphere topology) of plane bipolar triangula tions.\n\nThis is a joint work with Mickael Maazoun.\n LOCATION:https://stable.researchseminars.org/talk/Probability/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kolesnikov (HSE) DTSTART:20201026T201500Z DTEND:20201026T211500Z DTSTAMP:20260404T094122Z UID:Probability/8 DESCRIPTION:Title: Blaschke--Santalo inequality for many functions and geodesic ba rycenters of measures\nby Alexander Kolesnikov (HSE) as part of MIT pr obability seminar\n\n\nAbstract\nMotivated by the geodesic barycenter prob lem from optimal transportation theory\, we prove a natural generalization of the Blaschke–Santalo inequality for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem.\n \nThe talk is based on joint works with Elis abeth Werner.\n LOCATION:https://stable.researchseminars.org/talk/Probability/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Damron (Georgia Tech) DTSTART:20201102T211500Z DTEND:20201102T221500Z DTSTAMP:20260404T094122Z UID:Probability/9 DESCRIPTION:Title: Critical first-passage percolation in two dimensions\nby Mi chael Damron (Georgia Tech) as part of MIT probability seminar\n\n\nAbstra ct\nIn 2d first-passage percolation (FPP)\, we place nonnegative i.i.d. w eights (te) on the edges of ℤ2 and study the induced weighted graph pseudometric T=T(x\,y). If we denote by p=ℙ(te=0)\, then there is a tr ansition in the large-scale behavior of the model as p varies from 0 t o 1. When p<12\, T(0\,x) grows linearly in x\, and when p>12\, it is stochastically bounded. The critical case\, where p=12\, is more subtle\ , and the sublinear growth of T(0\,x) depends on the behavior of the dis tribution function of te near zero. I will discuss my work over the past few years that (a) determines the exact rate of growth of T(0\,x)\, (b) determines the ``time constant'' for the site-FPP model on the triangular lattice and\, more recently (c) studies the growth of T(0\,x) in a dynam ical version of the model\, where weights are resampled according to indep endent exponential clocks. These are joint works with J. Hanson\, D. Harpe r\, W.-K. Lam\, P. Tang\, and X. Wang.\n LOCATION:https://stable.researchseminars.org/talk/Probability/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Atilla Yilmaz (Temple) DTSTART:20201109T211500Z DTEND:20201109T221500Z DTSTAMP:20260404T094122Z UID:Probability/10 DESCRIPTION:Title: Stochastic homogenization of Hamilton-Jacobi equations in one dimension\nby Atilla Yilmaz (Temple) as part of MIT probability semina r\n\n\nAbstract\nAfter giving an introduction to the homogenization of Ham ilton-Jacobi (HJ) equations\, I will focus on HJ equations in one space di mension with Hamiltonians of the form G(p)+βV(x\,ω)\, where V is a st ationary & ergodic potential of unit amplitude. The homogenization of such equations is established in a 2016 paper of Armstrong\, Tran and Yu for a ll continuous and coercive G. Under the extra condition that G is a dou ble-well function (for the sake of clarity and convenience)\, I will prese nt a new and fully constructive proof of homogenization which yields a for mula for the effective Hamiltonian H‾‾ and clarifies the dependence of H‾‾ on G\, β and the law of V.\n LOCATION:https://stable.researchseminars.org/talk/Probability/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Subhabrata Sen (Harvard) DTSTART:20201116T211500Z DTEND:20201116T221500Z DTSTAMP:20260404T094122Z UID:Probability/11 DESCRIPTION:Title: Large deviations for dense random graphs: beyond mean-field\nby Subhabrata Sen (Harvard) as part of MIT probability seminar\n\n\nAbs tract\nIn a seminal paper\, Chatterjee and Varadhan derived an LDP for the dense Erdős-Rényi random graph\, viewed as a random graphon. This direc tly provides LDPs for continuous functionals such as subgraph counts\, spe ctral norms\, etc. In contrast\, very little is understood about this prob lem if the underlying random graph is inhomogeneous or constrained\n\nIn t his talk\, we will explore large deviations for dense random graphs\, beyo nd the ``mean-field" setting. In particular\, we will study large deviatio ns for uniform random graphs with given degrees\, and a family of dense bl ock model random graphs. We will establish the LDP in each case\, and iden tify the rate function. In the block model setting\, we will use this LDP to study the upper tail problem for homomorphism densities of regular sub- graphs. Our results establish that this problem exhibits a symmetry/symmet ry-breaking transition\, similar to one observed for Erdős-Rényi random graphs.\n\nBased on joint works with Christian Borgs\, Jennifer Chayes\, S ouvik Dhara\, Julia Gaudio and Samantha Petti.\n LOCATION:https://stable.researchseminars.org/talk/Probability/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Benson Au (UCSD) DTSTART:20201207T211500Z DTEND:20201207T221500Z DTSTAMP:20260404T094122Z UID:Probability/13 DESCRIPTION:Title: Finite-rank perturbations of random band matrices via infinite simal free probability\nby Benson Au (UCSD) as part of MIT probability seminar\n\n\nAbstract\nFree probability provides a unifying framework for studying random multi-matrix models in the large N limit. Typically\, the purview of these techniques is limited to invariant or mean-field ensembl es.\n Nevertheless\, we show that random band matrices fit quite naturally in this framework. Our considerations extend to the infinitesimal level\, where finer results can be stated for the 1/N correction. Our results all ow us to extend previous work of Shlyakhtenko\n on finite-rank perturbatio ns of Wigner matrices in the infinitesimal framework. For finite-rank pert urbations of our model\, we find outliers at the classical positions from the deformed Wigner ensemble.\n LOCATION:https://stable.researchseminars.org/talk/Probability/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Russell Lyons (Indiana University) DTSTART:20200914T201500Z DTEND:20200914T211500Z DTSTAMP:20260404T094122Z UID:Probability/15 DESCRIPTION:Title: Random Walks on Dyadic Lattice Graphs and Their Duals\nby Russell Lyons (Indiana University) as part of MIT probability seminar\n\n\ nAbstract\nDyadic lattice graphs and their duals are commonly used as disc rete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk\, but w hose duals have only a singular stationary measure. This answers a questio n of Curien and shows behaviour different from the unimodular case. The co nsequence is that planar duality does not combine well with stationary ran dom graphs. We also study harmonic measure on dyadic lattice graphs and sh ow its singularity. Much interesting behaviour observed numerically remain s to be explained. No background will be assumed for the talk. This is joi nt work with Graham White.\n\nDate: Monday\, September 14. \nTime: There w ill be an informal discussion for MIT local people with our speaker starti ng at 4 pm and the talk starts at the usual time 4:15 pm. Welcome to join the discussion before the talk and to say hi to the speaker and other atte ndees.\n\nZoom: https://mit.zoom.us/j/96421029678?pwd=cThIR2hVNUNpY1JDOS95 RUpoeFpmdz09​\n\nPassword: 356815\n\nPlease download and import the foll owing iCalendar (.ics) files to your calendar system.\nhttps://mit.zoom.us /meeting/tJIpdeiorDIsHdxRBXOnKJeRp0PlkQLDSHeo/ics?icsToken=98tyKuCuqjkrGta cth6PRowABojod_TzplhdgqdFrj3dLC54SAbEJrJyPrlOPPzj\n\n\nYou can check out m ore details about the seminar at https://math.mit.edu/seminars/probability /\n\nHope you see you on Monday\,\nYilin\n LOCATION:https://stable.researchseminars.org/talk/Probability/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Christophe Mourrat (New York University) DTSTART:20201019T201500Z DTEND:20201019T211500Z DTSTAMP:20260404T094122Z UID:Probability/16 DESCRIPTION:Title: Mean-field spin glasses: beyond the replica trick?\nby Jea n-Christophe Mourrat (New York University) as part of MIT probability semi nar\n\n\nAbstract\nSpin glasses are models of statistical mechanics encodi ng disordered interactions between many simple units. One of the fundament al quantities of interest is the free energy of the model\, in the limit w hen the number of units tends to infinity. For a restricted class of model s\, this limit was predicted by Parisi\, and later rigorously proved by Gu erra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partia l results suggesting that this new point of view may allow to understand l imit free energies for a larger class of models\, focusing in particular o n the case in which the units are organized over two layers\, and only int eract across layers.\n LOCATION:https://stable.researchseminars.org/talk/Probability/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Mikulincer (Weizmann Institute) DTSTART:20201130T191500Z DTEND:20201130T201500Z DTSTAMP:20260404T094122Z UID:Probability/17 DESCRIPTION:Title: Functional inequalities in Gauss space\nby Dan Mikulincer (Weizmann Institute) as part of MIT probability seminar\n\n\nAbstract\nWe will discuss how several known functional inequalities\, such as log-Sobol ev and Shannon-Stam\, arise from general principles in stochastic analysis . This point of view will give rise to a unified framework from which one may study the stability of those inequalities. Several results in this dir ection will be presented with further applications to central limit theore ms\, normal approximations and optimal transport.\n\nOur method is based o n an entropy-minimizing process from stochastic control theory\, which all ows us to express entropy as a solution to a variational problem.\n\nBased on joint works with Ronen Eldan\, Alex Zhai and Yair Shenfeld\n LOCATION:https://stable.researchseminars.org/talk/Probability/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Hariharan Narayanan (TIFR\, Mumbai) DTSTART:20210222T161500Z DTEND:20210222T171500Z DTSTAMP:20260404T094122Z UID:Probability/18 DESCRIPTION:Title: Random discrete concave functions on an equilateral lattice wi th periodic boundary conditions\nby Hariharan Narayanan (TIFR\, Mumbai ) as part of MIT probability seminar\n\n\nAbstract\nMotivated by connectio ns to random matrices\, Littlewood-Richardson coefficients and square-tria ngle tilings\, we study random discrete concave functions on an equilatera l lattice\, where the Hessian satisfies periodic boundary conditions and h as a given average s. Defining surface tension sigma to be the negative of a certain limiting differential entropy per site\, we show that sigma is a well defined convex function of s. When s is such that sigma is strictly convex\, we show that the corresponding rescaled random surfaces concentr ate in the sup norm as the length scale of the periodicity n tends to infi nity. We also show that concentration occurs when the gradient of sigma be longs to a certain cone\, and in this case obtain quantitative bounds for the concentration.\n\nA preprint can be found at https://arxiv.org/abs/20 05.13376 .\n LOCATION:https://stable.researchseminars.org/talk/Probability/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Alberts (University of Utah) DTSTART:20210301T211500Z DTEND:20210301T221500Z DTSTAMP:20260404T094122Z UID:Probability/19 DESCRIPTION:Title: Loewner Dynamics for the Multiple SLE(0) Process\nby Tom A lberts (University of Utah) as part of MIT probability seminar\n\n\nAbstra ct\nRecently Peltola and Wang introduced the multiple SLE(0) process as th e deterministic limit of the random multiple SLE(κ) curves as κ goes to zero. They prove this result by means of a ``small κ" large deviations pr inciple\, but the limiting curves also turn out to have important geometri c characterizations that are independent of their relation to SLE(κ). In particular\, they show that the SLE(0) curves can be generated by a determ inistic Loewner evolution driven by multiple points\, and the vector field describing the evolution of these points must satisfy a particular system of algebraic equations. We show how to generate solutions to these algebr aic equations in two ways: first in terms of the poles and critical points of an associated real rational function\, and second via the well-known C alogero-Moser integrable system with particular initial velocities. Althou gh our results are purely deterministic they are again motivated by taking limits of probabilistic constructions\, which I will explain.\n LOCATION:https://stable.researchseminars.org/talk/Probability/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin McKenna (NYU) DTSTART:20210315T201500Z DTEND:20210315T211500Z DTSTAMP:20260404T094122Z UID:Probability/20 DESCRIPTION:Title: Random determinants and landscape complexity beyond invariance \nby Benjamin McKenna (NYU) as part of MIT probability seminar\n\n\nAb stract\nThe Kac-Rice formula allows one to study the complexity of high-di mensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present a new r esult on determinant asymptotics for non-invariant random matrices\, and u se it to compute (annealed) complexity for several types of landscapes. Th ese include (i) the elastic manifold\, where we identify the "Larkin mass" separating order and disorder\, verifying results of Fyodorov-Le Doussal\ , and (ii) soft spins in an anisotropic well\, where we find a new phase t ransition with universal quadratic and cubic near-critical behavior. This extends the pioneering complexity results of Fyodorov and Auffinger-Ben Ar ous-Cerny. Joint work with Gerard Ben Arous and Paul Bourgade.\n LOCATION:https://stable.researchseminars.org/talk/Probability/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Shirshendu Ganguly (UC Berkeley) DTSTART:20210322T201500Z DTEND:20210322T211500Z DTSTAMP:20260404T094122Z UID:Probability/21 DESCRIPTION:Title: Stability and chaos in dynamical last passage percolation\ nby Shirshendu Ganguly (UC Berkeley) as part of MIT probability seminar\n\ n\nAbstract\nMany complex disordered systems in statistical mechanics are characterized by intricate energy landscapes. The ground state\, the confi guration with the lowest energy\, lies at the base of the deepest valley. In important examples\, such as Gaussian polymers and spin glass models\, the landscape has many valleys and the abundance of near-ground states (at the base of the valleys) indicates the phenomenon of chaos\, under which the ground state alters profoundly when the disorder of the model is sligh tly perturbed.\n\nIn this talk\, we will discuss a recent work with Alan H ammond computing the critical exponent that governs the onset of chaos in a dynamic manifestation of a canonical planar last passage percolation mod el in the Kardar-Parisi-Zhang universality class. We expect this exponent to be universal across a wide range of interface and stochastic growth mod els. The arguments rely on Chatterjee's harmonic analytic theory of equiva lence of super-concentration and chaos in Gaussian spaces and a refined un derstanding of the corresponding static landscape geometry.\n LOCATION:https://stable.researchseminars.org/talk/Probability/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio (Tuca) Auffinger (Northwestern) DTSTART:20210329T140000Z DTEND:20210329T150000Z DTSTAMP:20260404T094122Z UID:Probability/22 DESCRIPTION:Title: TAP equations and ground states of generalized spin glass mode ls\nby Antonio (Tuca) Auffinger (Northwestern) as part of MIT probabil ity seminar\n\n\nAbstract\nIn this talk\, I will survey models of spin gla sses where the spins take values either in a ball in $\\mathbb R^d$ or in a large subset of the integers. I will discuss two important quantities: t he TAP equations\, a system of self-consistent equations relating the spin magnetization at high temperature\, and the ground-state energy\, the min imum of the Hamiltonian. During the talk\, I will stress the differences a nd the new difficulties that appear when one compares these models to clas sical models such as the Sherrington-Kirkpatrick or the spherical p-spin m odel. Based on joint works with Cathy Chen (Northwestern) and Yuxin Zhou ( Northwestern).\n\nSeminar Zoom link: https://mit.zoom.us/j/96421029678?pwd =cThIR2hVNUNpY1JDOS95RUpoeFpmdz09​ \n\nPassword: 356815​\n\nSeminar w ebpage: https://math.mit.edu/probability/\n\nSeminar Zoom link: https://mi t.zoom.us/j/96421029678?pwd=cThIR2hVNUNpY1JDOS95RUpoeFpmdz09​ \n\nPassw ord: 356815​\n\nSeminar webpage: https://math.mit.edu/probability/\n LOCATION:https://stable.researchseminars.org/talk/Probability/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Masha Gordina (UConn) DTSTART:20210405T201500Z DTEND:20210405T211500Z DTSTAMP:20260404T094122Z UID:Probability/23 DESCRIPTION:Title: Uniform volume doubling and functional inequalities on Lie gro ups\nby Masha Gordina (UConn) as part of MIT probability seminar\n\n\n Abstract\nOn a compact Lie group with a left-invariant Riemannian metric\, many important functional inequalities for the Laplacian (such as Poincar \\'e inequality\, parabolic Harnack inequality\, etc.)  can be proved usi ng only the volume doubling property.  That is\,  constants in these ine qualities can be controlled by the doubling constant of the metric\; this can be strictly more powerful than classical techniques involving Ricci cu rvature lower bounds.  It can happen that there is a uniform bound on the doubling constants of all left-invariant metrics on a given Lie group\; s uch a group is called uniformly doubling.  In such a case\, the implicit constants in the functional inequalities will also be uniformly bounded ov er all left-invariant metrics.  We show that this happens for the special unitary group SU(2)\, via explicit uniform volume estimates and describe the consequences (heat kernel estimates\, Weyl counting function etc)\n\nT his is joint work with Nate Eldredge and Laurent Saloff-Coste.\n LOCATION:https://stable.researchseminars.org/talk/Probability/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Dauvergne (Princeton) DTSTART:20210412T201500Z DTEND:20210412T211500Z DTSTAMP:20260404T094122Z UID:Probability/24 DESCRIPTION:Title: The directed landscape.\nby Duncan Dauvergne (Princeton) a s part of MIT probability seminar\n\n\nAbstract\nThe directed landscape is a random `directed metric' on the spacetime plane that arises as the scal ing limit of integrable models of last passage percolation. It is expected to be the universal scaling limit for all models in the KPZ universality class for random growth. In this talk\, I will describe its construction i n terms of the Airy line ensemble\, give an extension of this construction for optimal length disjoint paths\, and discuss probabilistic consequence s of these constructions. Based on joint work with J. Ortmann\, B. Virag\, and L. Zhang.\n LOCATION:https://stable.researchseminars.org/talk/Probability/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Shriver (UCLA) DTSTART:20210426T201500Z DTEND:20210426T211500Z DTSTAMP:20260404T094122Z UID:Probability/25 DESCRIPTION:Title: Free energy\, Gibbs measures\, and Glauber dynamics on trees\nby Christopher Shriver (UCLA) as part of MIT probability seminar\n\n\n Abstract\nI will introduce some ideas from sofic entropy theory and use th em to define a notion of free energy density in the context of finite-alph abet\, nearest-neighbor interactions (like the Ising model) indexed by inf inite regular trees. This free energy is used to prove that shift-invarian t measures are Gibbs if and only if they are Glauber-invariant. We also es tablish a metastability phenomenon for the corresponding dynamics on finit e locally-tree-like regular graphs. These results can be combined to chara cterize maximal-entropy joinings of Gibbs measures.\n LOCATION:https://stable.researchseminars.org/talk/Probability/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Youngtak Sohn (Stanford) DTSTART:20210503T201500Z DTEND:20210503T211500Z DTSTAMP:20260404T094122Z UID:Probability/26 DESCRIPTION:Title: Replica symmetry breaking for random regular NAE-SAT\nby Y oungtak Sohn (Stanford) as part of MIT probability seminar\n\n\nAbstract\n In a wide class of random constraint satisfaction problems\, ideas from st atistical physics predict that there is a rich set of phase transitions go verned by one-step replica symmetry breaking(1RSB). In particular\, it is conjectured that there is the condensation regime below the satisfiability threshold\, where the solution space condenses into the large clusters. W e establish this phenomenon for the random regular NAE-SAT model by showin g that most of the solutions lie in a bounded number of clusters and the o verlap of two independent solutions concentrates on two points. Central to the proof is to calculate the moments of the number of clusters whose siz e is in an O(1) window.\n LOCATION:https://stable.researchseminars.org/talk/Probability/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Morris (Jie Jun) Ang (MIT) DTSTART:20210510T201500Z DTEND:20210510T211500Z DTSTAMP:20260404T094122Z UID:Probability/27 DESCRIPTION:Title: Integrability of the conformal loop ensemble\nby Morris (J ie Jun) Ang (MIT) as part of MIT probability seminar\n\n\nAbstract\nFor $\ \frac{8}{3} < \\kappa < 8$\, the conformal loop ensemble $\\mathrm{CLE}_{\ \kappa}$ is a canonical random ensemble of loops which is conformally inva riant in law\, and whose loops locally look like Schramm-Loewner evolution with parameter $\\kappa$. It describes the scaling limits of the Ising mo del\, percolation\, and other models. When $\\kappa \\leq 4$ the loops are simple curves. In this regime\, we compute the three-point function of $\ \mathrm{CLE}_{\\kappa}$ on the sphere and show it agrees with the imaginar y DOZZ formula of Zamolodchikov (2005). We also verify a conjecture of Ken yon and Wilson on the electrical thickness of $\\mathrm{CLE}_{\\kappa}$ on the sphere. Our arguments depend on couplings of $\\mathrm{CLE}$ with Lio uville quantum gravity and the integrability of Liouville conformal field theory.\nBased on joint work with Xin Sun\, which builds on our recent wor k with Holden and Remy.\n LOCATION:https://stable.researchseminars.org/talk/Probability/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Minjae Park (MIT) DTSTART:20210517T201500Z DTEND:20210517T211500Z DTSTAMP:20260404T094122Z UID:Probability/28 DESCRIPTION:Title: Wilson loop expectations as sums over surfaces in 2D\nby M injae Park (MIT) as part of MIT probability seminar\n\n\nAbstract\nAlthoug h lattice Yang-Mills theory on $\\mathbb Z^d$ is easy to rigorously define \, the construction of a satisfactory continuum theory on $\\mathbb R^d$ i s a major open problem when $d \\geq 3$. Such a theory should assign a Wil son loop expectation to each collection of loops in $\\mathbb R^d$. One of the proposed approaches involves representing this quantity as a sum over surfaces having the loops as their boundary. There are some formal/heuris tic ways to make sense of this notion\, but they typically yield an ill-de fined difference of infinities. The goal of this talk is to make sense of Yang-Mills integrals as surface sums in the special case that $d=2$\, wher e the existence of a well-defined continuum theory is already well known. We also obtain an alternative proof of the Makeenko-Migdal equation\, and Levy's formula based on the Schur-Weyl duality.\n\nJoint work with Joshua Pfeffer\, Scott Sheffield\, and Pu Yu.\n LOCATION:https://stable.researchseminars.org/talk/Probability/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Jimmy He (MIT) DTSTART:20210913T201500Z DTEND:20210913T211500Z DTSTAMP:20260404T094122Z UID:Probability/29 DESCRIPTION:Title: Random walks on finite fields with deterministic jumps\nby Jimmy He (MIT) as part of MIT probability seminar\n\nLecture held in Room : 2-147 in the Simons Building.\n\nAbstract\nRecently\, Chatterjee and Dia conis showed that most bijections\, if applied between steps of a Markov c hain\, cause the resulting chain to mix much faster. However\, explicit ex amples of this speedup phenomenon are rare. I will discuss recent work stu dying such walks on finite fields where the bijection is algebraically def ined. This work gives a large collection of examples where this speedup ph enomenon occurs. These walks can be seen as a non-linear analogue of the C hung-Diaconis-Graham process\, where the bijection is multiplication by a non-zero element of the finite field. This work is partially joint with Hu y Pham and Max Xu.\n LOCATION:https://stable.researchseminars.org/talk/Probability/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Yves Gaudreau Lamarre (University of Chicago) DTSTART:20210920T201500Z DTEND:20210920T211500Z DTSTAMP:20260404T094122Z UID:Probability/30 DESCRIPTION:Title: Number rigidity in the spectrum of random Schrödinger operato rs\nby Pierre Yves Gaudreau Lamarre (University of Chicago) as part of MIT probability seminar\n\n\nAbstract\nIn this talk\, I will discuss rece nt progress in the understanding of the structure in the spectrum of rando m Schrödinger operators. More specifically\, I will introduce the concept of number rigidity in point processes and discuss recent efforts to under stand its occurrence in the spectrum of random Schrödinger operators. Bas ed on joint works with Promit Ghosal (MIT)\, Wenxuan Li (UChicago)\, and Y uchen Liao (Warwick).\n LOCATION:https://stable.researchseminars.org/talk/Probability/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lisa Sauermann (MIT) DTSTART:20210927T201500Z DTEND:20210927T211500Z DTSTAMP:20260404T094122Z UID:Probability/31 DESCRIPTION:Title: On the extension complexity of random polytopes.\nby Lisa Sauermann (MIT) as part of MIT probability seminar\n\nLecture held in Room : 2 - 147 in the Simons Building.\n\nAbstract\nSometimes\, it is possible to represent a complicated polytope as a projection of a much simpler poly tope. To quantify this phenomenon\, the extension complexity of a polytope P is defined to be the minimum number of facets in a (possibly higher-dim ensional) polytope from which P can be obtained as a (linear) projection. In this talk\, we discuss some results on the extension complexity of rand om polytopes. For a fixed dimension d\, we consider random d-dimensional p olytopes obtained as the convex hull of independent random points either i n the unit ball ball or on the unit sphere. In both cases\, we prove that the extension complexity is typically on the order of the square root of n umber of vertices of the polytope. Joint work with Matthew Kwan and Yufei Zhao.\n LOCATION:https://stable.researchseminars.org/talk/Probability/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Cook (Duke) DTSTART:20211004T201500Z DTEND:20211004T211500Z DTSTAMP:20260404T094122Z UID:Probability/32 DESCRIPTION:Title: Large deviations and regularity method for sparse random hyper graphs\nby Nick Cook (Duke) as part of MIT probability seminar\n\n\nAb stract\nThe "infamous upper tail" problem for subgraph counts in Erdős– Rényi graphs has received considerable attention since it was popularized by Janson and Rucinski\, and has connections with questions in graph limi t theory and statistical physics. I will survey work in this area and disc uss a new approach for the more general setting of hypergraphs\, based on an extension of the regularity method to sparse hypergraphs. In particular \, we develop a sparse counting lemma and decomposition theorem for tensor s under a novel class of norms that generalize the matrix cut norm. Based on joint work with Amir Dembo and Huy Tuan Pham.\n LOCATION:https://stable.researchseminars.org/talk/Probability/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Matan Harel (Northeastern University) DTSTART:20211018T201500Z DTEND:20211018T211500Z DTSTAMP:20260404T094122Z UID:Probability/33 DESCRIPTION:Title: Quantitative estimates on the effect of random disorder on low -dimensional lattice models\nby Matan Harel (Northeastern University) as part of MIT probability seminar\n\nLecture held in MIT Room 2-147.\n\nA bstract\nIn their seminal work\, Imry and Ma predicted that the addition o f an arbitrarily small random external field to a low-dimensional statisti cal physics model causes the usual first-order phase transition to be `rou nded-off.' This phenomenon was proven rigorously by Aizenman and Wehr in 1 989 for a vastly general class of spin systems and random perturbations. R ecently\, the effect was quantified for the random-field Ising model\, pro ving that it exhibits exponential decay of correlations at all temperature s. Unfortunately\, the analysis relies on the monotonicity (FKG) propertie s which are not present in many other classical models of interest. This t alk will present quantitative versions of the Aizenman-Wehr theorems for g eneral spin systems with random disorder\, including Potts\, spin O(n)\, s pin glasses\, and random surface models. This is joint work with Paul Dari o and Ron Peled.\n LOCATION:https://stable.researchseminars.org/talk/Probability/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Bates (Wisconsin) DTSTART:20211025T201500Z DTEND:20211025T211500Z DTSTAMP:20260404T094122Z UID:Probability/34 DESCRIPTION:Title: Empirical measures\, geodesic lengths\, and a variational form ula in first-passage percolation.\nby Erik Bates (Wisconsin) as part o f MIT probability seminar\n\n\nAbstract\nWe consider the standard first-pa ssage percolation model on Z^d\, in which each edge is assigned an i.i.d. nonnegative weight\, and the passage time between any two points is the sm allest total weight of a nearest-neighbor path between them. Our primary i nterest is in the empirical measures of edge-weights observed along geodes ics from 0 to [n\\xi]\, where \\xi is a fixed unit vector. For various den se families of edge-weight distributions\, we prove that these measures co nverge weakly to a deterministic limit as n tends to infinity. The key too l is a new variational formula for the time constant. In this talk\, I wil l derive this formula and discuss its implications for the convergence of both empirical measures and lengths of geodesics.\n LOCATION:https://stable.researchseminars.org/talk/Probability/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Dunlap (NYU Courant) DTSTART:20211108T211500Z DTEND:20211108T221500Z DTSTAMP:20260404T094122Z UID:Probability/35 DESCRIPTION:Title: Fluctuations of solutions to the KPZ equation on a large torus \nby Alex Dunlap (NYU Courant) as part of MIT probability seminar\n\nL ecture held in Seminar in Simon's Building room: 2-147.\n\nAbstract\nI wil l discuss proofs of optimal (up to constants) variance bounds on the solut ions to the KPZ equation on a torus\, as the time scale and the size of th e torus are taken to infinity together\, in the super-relaxation regime an d part of the relaxation regime. The arguments are based on stochastic ana lysis and do not use a connection to a discrete system. Joint work with Yu Gu and Tomasz Komorowski.\n LOCATION:https://stable.researchseminars.org/talk/Probability/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Han Huang (Georgia Tech) DTSTART:20211115T211500Z DTEND:20211115T221500Z DTSTAMP:20260404T094122Z UID:Probability/36 DESCRIPTION:Title: Title to be announced\nby Han Huang (Georgia Tech) as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Probability/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Ellen Powell (Durham) DTSTART:20211122T211500Z DTEND:20211122T221500Z DTSTAMP:20260404T094122Z UID:Probability/37 DESCRIPTION:Title: Brownian excursions\, conformal loop ensembles and critical Li ouville quantum gravity\nby Ellen Powell (Durham) as part of MIT proba bility seminar\n\n\nAbstract\nIn a groundbreaking work\, Duplantier\, Mill er and Sheffield showed that subcritical Liouville quantum gravity (LQG) c oupled with Schramm-Loewner evolutions (SLE) can be described by the matin g of two continuum random trees. In this talk I will discuss the counterpa rt of their result for critical LQG and SLE. More precisely\, I will expla in how\, as we approach criticality from the subcritical regime\, the spac e-filling SLE degenerates to the uniform CLE_4 exploration introduced by W erner and Wu\, together with a collection of independent coin tosses index ed by the branch points of the exploration. Furthermore\, although the pai r of continuum random trees collapse to a single continuum random tree in the limit we can apply an appropriate affine transform to the encoding Bro wnian motions before taking the limit\, and get convergence to a Brownian half-plane excursion. I will try to explain how observables of interest in the critical CLE decorated LQG picture are encoded by a growth fragmentat ion naturally embedded in the Brownian excursion. This talk is based on jo int work with Juhan Aru\, Nina Holden and Xin Sun.\n LOCATION:https://stable.researchseminars.org/talk/Probability/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lingfu Zhang (Princeton) DTSTART:20211129T211500Z DTEND:20211129T221500Z DTSTAMP:20260404T094122Z UID:Probability/38 DESCRIPTION:Title: The environment seen from a geodesic in last-passage percolati on.\nby Lingfu Zhang (Princeton) as part of MIT probability seminar\n\ n\nAbstract\nIn exponential directed last-passage percolation\, each verte x in $Z^2$ is assigned an i.i.d. exponential weight\, and the geodesic bet ween a pair of vertices refers to the up-right path connecting them\, with the maximum total weight along the path. It is a natural question to ask what a geodesic looks like locally\, and how weights on and nearby the geo desic behave. In this talk\, I will present some new results on this. We s how convergence of the distribution of the ‘environment’ as seen from a typical point along the geodesic\, and convergence of the corresponding empirical measure\, as the geodesic length goes to infinity. In addition\, we obtain an explicit description of the limiting environment\, which dep ends on the direction of the geodesic. This in principle enables one to co mpute all the local statistics of the geodesic\, and I will talk about som e surprising and interesting examples. This is based on joint work with Ja mes Martin and Allan Sly.\n LOCATION:https://stable.researchseminars.org/talk/Probability/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Yury Polyansky (MIT) DTSTART:20211206T211500Z DTEND:20211206T221500Z DTSTAMP:20260404T094122Z UID:Probability/39 DESCRIPTION:Title: Uniqueness of BP fixed point for Ising models.\nby Yury Po lyansky (MIT) as part of MIT probability seminar\n\n\nAbstract\nIn the stu dy of Ising models on large locally tree-like graphs\, in both rigorous an d non-rigorous methods one is often led to understanding the so-called bel ief propagation distributional recursions and its fixed point (also known as Bethe fixed point\, cavity equation etc). In this work we prove there i s at most one non-trivial fixed point for Ising models with zero or random (but ``unbiased'') external fields.\n
\n
\n As a concrete example\, consider a sample A of Ising model on a rooted t ree (regular\, Galton-Watson\, etc). Let B be a noisy version of A obtaine d by independently perturbing each spin as follows: $B_v$ equals to $A_v$ with some small probability $\\delta$ and otherwise taken to be a uniform +-1 (alternatively\, 0). We show that the distribution of the root spin $A_\\rho$ conditioned on values $B_v$ of all vertices $v$ at a large dista nce from the root is independent of $\\delta$ and coincides with $\\delta= 0$. Previously this was only known for sufficiently ``low-temperature'' m odels. Our proof consists of constructing a metric under which the BP oper ator is a contraction (albeit non-multiplicative). I hope to convince you our proof is technically rather simple.\n
\n
\n This simultaneously closes the following 5 conjectures in the literat ure:\n
\n
    \n
  1. uselessness of global inf ormation for a labeled 2-community stochastic block model\, or 2-SBM (Kana de-Mossel-Schramm'2014)\;
    2. \n
  2. opt imality of local algorithms for 2-SBM under noisy side information (Mossel -Xu'2015)\;
    3. \n
  3. independence of r obust reconstruction accuracy to leaf noise in broadcasting on trees (Moss el-Neeman-Sly'2016)\;
    4. \n
  4. boundar y irrelevance in BOT (Abbe-Cornacchia-Gu-P.'2021)\;
    5. \n
  5. characterization of entropy of community labels giv en the graph in 2-SBM (ibid).
    6. \n
\n
\n \n Joint work with Qian Yu (Princeton).

\n LOCATION:https://stable.researchseminars.org/talk/Probability/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Hilario (UFMG) DTSTART:20211101T201500Z DTEND:20211101T211500Z DTSTAMP:20260404T094122Z UID:Probability/40 DESCRIPTION:Title: Random walks on dynamic random environments with non-uniform m ixing.\nby Marcelo Hilario (UFMG) as part of MIT probability seminar\n \n\nAbstract\nIn this talk\, we will discuss recent results on the limitin g behavior of random walks in dynamic random environments. We will mainly discuss the case when the random walk evolves on one-dimensional random en vironments given by conservative interacting particle systems such as the simple symmetric exclusion process. Its transitions probabilities will dep end on the current occupation environment nearby. Conservation of particle s leads to poor mixing conditions and we explain how renormalization techn iques can be useful to obtain the law of large numbers\, large deviation e stimates\, and sometimes central limit theorems. The talk is based on seve ral joint works with Oriane Blondel\, Frank den Hollander\, Daniel Kious\, Renato dos Santos\, Vladas Sidoravicius and Augusto Teixeira.\n LOCATION:https://stable.researchseminars.org/talk/Probability/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Nishant Changotia (Tata Institute of Fundamental Research) DTSTART:20211213T211500Z DTEND:20211213T221500Z DTSTAMP:20260404T094122Z UID:Probability/41 DESCRIPTION:Title: Title to be announced\nby Nishant Changotia (Tata Institut e of Fundamental Research) as part of MIT probability seminar\n\n\nAbstrac t\nAbstract to be shared\n LOCATION:https://stable.researchseminars.org/talk/Probability/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Cole Graham (Brown University) DTSTART:20220214T211500Z DTEND:20220214T221500Z DTSTAMP:20260404T094122Z UID:Probability/42 DESCRIPTION:Title: Stationary measures for stochastic conservation laws\nby C ole Graham (Brown University) as part of MIT probability seminar\n\n\nAbst ract\n\\noindent At long times\, many SPDEs relax to statistically steady states. In this talk\, I will consider the existence and uniqueness of suc h stationary measures for stochastically-forced viscous conservation laws on the line. A special case\, the stochastic Burgers equation\, has receiv ed a great deal of attention due to its links to the KPZ and stochastic he at equations. Stochastic Burgers is known to admit a unique spacetime-stat ionary ergodic measure for each mean. However\, existing proofs rely on th e Cole–Hopf transformation\, which does not extend to other conservation laws. I will discuss a comparison-based approach that recovers partial re sults for more general conservation laws. In particular\, such SPDEs admit infinitely many stationary ergodic measures\, and there is at most one su ch measure for each mean. \\\\\n\\vspace{2ex}\n\\noindent This is joint wo rk with Theodore Drivas\, Alexander Dunlap\, Joonhyun La\, and Lenya Ryzhi k.\n LOCATION:https://stable.researchseminars.org/talk/Probability/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Sellke (Stanford University) DTSTART:20220307T211500Z DTEND:20220307T221500Z DTSTAMP:20260404T094122Z UID:Probability/43 DESCRIPTION:Title: Algorithmic Thresholds in Mean-Field Spin Glasses\nby Mark Sellke (Stanford University) as part of MIT probability seminar\n\nLectur e held in Room 2-147 in the Simons Building.\n\nAbstract\n\\noindent I wil l explain recent progress on computing approximate ground states of mean-f ield spin glass Hamiltonians\, which are certain random functions in high dimension. While the asymptotic ground state energy OPT is given by the fa mous Parisi formula\, the landscape of these functions often include many bad local optima which impede optimization by efficient algorithms. In the positive direction\, I will explain algorithms based on approximate messa ge passing which asymptotically achieve a value ALG given by an extended P arisi formula. The case ALG=OPT has a "no overlap gap" or "full replica sy mmetry breaking" interpretation\, but in general these algorithms may fail to reach asymptotic optimality. In the negative direction\, I will explai n why no algorithm with suitably Lipschitz dependence on the random disord er can surpass the threshold ALG. This result applies to many standard opt imization algorithms\, such as gradient descent and its variants on dimens ion-free time scales. Based on joint works with Ahmed El Alaoui\, Brice Hu ang\, and Andrea Montanari.\n LOCATION:https://stable.researchseminars.org/talk/Probability/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Oanh Nguyen (Brown University) DTSTART:20220328T201500Z DTEND:20220328T211500Z DTSTAMP:20260404T094122Z UID:Probability/44 DESCRIPTION:Title: Survival time of the contact process on random graphs\nby Oanh Nguyen (Brown University) as part of MIT probability seminar\n\nLectu re held in Room 2-147 in the Simons Building.\n\nAbstract\n\\noindent The contact process is a model for the spread of infections on graphs. In this talk\, we discuss the contact process on random graphs with low infection rate $\\lambda$. For random $d$-regular graphs\, it is known that the sur vival time is $O(\\log n)$ below the critical $\\lambda_c$. By contrast\, on the Erdos-Renyi random graphs $G(n\,d/n)$\, rare high degree vertices result in much longer survival times. We show that the survival time is go verned by high density local configurations\, in particular large connecte d components of high degree vertices on which the infection lasts for time $n^{\\lambda^{2+o(1)}}$. We shall discuss how to obtain a matching upper bound. Our methods\, moreover\, generalize to random graphs with given de gree distributions that have exponential moments.\\\\\n\\vspace{2ex}\n\\no indent Joint work with Allan Sly. \\\\\n LOCATION:https://stable.researchseminars.org/talk/Probability/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Alt (Courant Institute) DTSTART:20220404T201500Z DTEND:20220404T211500Z DTSTAMP:20260404T094122Z UID:Probability/45 DESCRIPTION:Title: Localization and Delocalization in Erdős–Rényi graphs\ nby Johannes Alt (Courant Institute) as part of MIT probability seminar\n\ nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\nWe consid er the Erdős–Rényi graph on N vertices with edge probability d/N. It i s well known that the structure of this graph changes drastically when d i s of order log N. Below this threshold it develops inhomogeneities which l ead to the emergence of localized eigenvectors\, while the majority of the eigenvectors remains delocalized. In this talk\, I will present the phase diagram depicting these localized and delocalized phases and our recent p rogress in establishing it rigorously.\n\nThis is based on joint works wit h Raphael Ducatez and Antti Knowles.\n LOCATION:https://stable.researchseminars.org/talk/Probability/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sky Cao (Stanford University) DTSTART:20220411T201500Z DTEND:20220411T211500Z DTSTAMP:20260404T094122Z UID:Probability/46 DESCRIPTION:Title: Exponential decay of correlations in finite gauge group lattic e gauge theories\nby Sky Cao (Stanford University) as part of MIT prob ability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nA bstract\nLattice gauge theories with finite gauge groups are statistical m echanical models\, very much akin to the Ising model\, but with some twist s. In this talk\, I will describe how to show exponential decay of correla tions for these models at low temperatures. This is based on joint work wi th Arka Adhikari.\n LOCATION:https://stable.researchseminars.org/talk/Probability/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Ahn (Cornell University) DTSTART:20220425T201500Z DTEND:20220425T211500Z DTSTAMP:20260404T094122Z UID:Probability/47 DESCRIPTION:Title: Lyapunov Exponents of Random Matrix Products and Brownian Moti on on GL(n\,C)\nby Andrew Ahn (Cornell University) as part of MIT prob ability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nA bstract\nConsider the discrete-time process formed by the singular values of products of random matrices\, where time corresponds to the number of m atrix factors. It is known due to Oseledets' theorem that under general as sumptions\, the Lyapunov exponents converge as the number of matrix factor s tend to infinity. In this talk\, we consider random matrices with distri butional invariance under right multiplication by unitary matrices\, which include Ginibre matrices and truncated unitary matrices. The correspondin g singular value process is Markovian with additional structure that admit s study via integrable probability techniques. In this talk\, I will discu ss recent results on the Lyapunov exponents in the setting where the numbe r M matrix factors tend to infinity simultaneously with matrix sizes N. Wh en this limit is tuned so that M and N grow on the same order\, the limiti ng Lyapunov exponents can be described in terms of Dyson Brownian motion w ith a special drift vector\, which in turn can be linked to a matrix-value d diffusion on the complex general linear group. We find that this descrip tion is universal\, under general assumptions on the spectrum of the matri x factors.\n LOCATION:https://stable.researchseminars.org/talk/Probability/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Massimiliano Gubinelli (University of Bonn) DTSTART:20220502T201500Z DTEND:20220502T211500Z DTSTAMP:20260404T094122Z UID:Probability/48 DESCRIPTION:Title: What is stochastic quantization?\nby Massimiliano Gubinell i (University of Bonn) as part of MIT probability seminar\n\n\nAbstract\nI n this talk I will introduce the idea of stochastic\nquantization from a m athematical perspective\, that is as a tool to\nanalyze rigorously Euclide an quantum fields. I will show that there\nare several different "stochast ic quantizations” for which we will\nidentify common structures and idea s which take the form of a\nstochastic analysis of Euclidean quantum field s.\n LOCATION:https://stable.researchseminars.org/talk/Probability/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Phil Sosoe (Cornell University) DTSTART:20220509T190000Z DTEND:20220509T200000Z DTSTAMP:20260404T094122Z UID:Probability/49 DESCRIPTION:Title: Almost-optimal regularity conditions in the CLT for Wigner mat rices.\nby Phil Sosoe (Cornell University) as part of MIT probability seminar\n\nLecture held in Room 2-361 in the Simons Building.\n\nAbstract\ nWe consider linear spectral statistics for test functions of low regulari ty and Wigner matrices with smooth entry distribution. We show that for fu nctions in the Sobolev space $H^{1/2 + \\epsilon}$ or the space $C^{1/2 + \\epsilon}$ that are supported within the spectral bulk of the semicircle distribution\, the variance remains bounded asymptotically. As a consequen ce\, these linear spectral statistics have asymptotic Gaussian fluctuation s with the same variance as in the CLT for functions of higher regularity\ , for any $\\epsilon > 0$. This result is nearly optimal in the sense that the variance does remain bounded for functions in $H^{1/2}$\, and was pre viously known only for matrices in Gaussian Unitary Ensemble.\n LOCATION:https://stable.researchseminars.org/talk/Probability/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Falconet (NYU) DTSTART:20220228T211500Z DTEND:20220228T221500Z DTSTAMP:20260404T094122Z UID:Probability/50 DESCRIPTION:Title: Metric growth dynamics in Liouville quantum gravity\nby Hu go Falconet (NYU) as part of MIT probability seminar\n\n\nAbstract\n\\noin dent Liouville quantum gravity (LQG) is a canonical model of random geomet ry. Associated with the planar Gaussian free field\, this geometry with sp ecial conformal symmetries was introduced in the physics literature by Pol yakov in the 80's and is conjectured to describe the scaling limit of rand om planar maps. In this talk\, I will introduce LQG as a metric measure sp ace and discuss recent results on the associated metric growth dynamics. T he primary focus will be on the dynamics of the trace of the free field on the boundary of growing LQG balls. \\\\\n\\vspace{2ex}\n\\noindent Based on a joint work with Julien Dubédat.\n LOCATION:https://stable.researchseminars.org/talk/Probability/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Eviatar Procaccia (Technion) DTSTART:20220314T170000Z DTEND:20220314T180000Z DTSTAMP:20260404T094122Z UID:Probability/51 DESCRIPTION:Title: Stationary Hastings-Levitov model\nby Eviatar Procaccia (T echnion) as part of MIT probability seminar\n\nLecture held in Room 2-132 in the Simons Building.\n\nAbstract\nWe construct and study a stationary v ersion of the Hastings-Levitov(0) model. We prove that unlike the classica l model\, in the stationary case\, particle sizes are tight\, yielding tha t this model can be seen as a tractable off-lattice Diffusion Limited Aggr egation (DLA). The stationary setting together with a geometric interpreta tions of the harmonic measure yields new geometric results such as finiten ess of arms\, exact growth rate and fractal dimension equals 3/2\, corresp onding to a numerical prediction of Meakin from 1983 for the gyration radi us of DLA growing on a long line segment. We will also show that similar r esults can be achieved in a cylinder.\n LOCATION:https://stable.researchseminars.org/talk/Probability/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Schmid (Princeton University) DTSTART:20220314T201500Z DTEND:20220314T211500Z DTSTAMP:20260404T094122Z UID:Probability/52 DESCRIPTION:Title: Mixing times for the TASEP on the circle\nby Dominik Schmi d (Princeton University) as part of MIT probability seminar\n\nLecture hel d in Room 2-147 in the Simons Building.\n\nAbstract\nThe exclusion process is one of the best-studied examples of an interacting particle system. In this talk\, we consider simple exclusion processes on finite graphs. We g ive an overview over some recent results on the mixing time of the totally asymmetric simple exclusion process (TASEP). In particular\, we provide b ounds on the mixing time of the TASEP on the circle\, using a connection t o periodic last passage percolation. This talk is based on joint work with Allan Sly (Princeton).\n LOCATION:https://stable.researchseminars.org/talk/Probability/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Rhodes (Aix-Marseille Université) DTSTART:20220425T170000Z DTEND:20220425T180000Z DTSTAMP:20260404T094122Z UID:Probability/53 DESCRIPTION:Title: Segal’s axioms and conformal bootstrap in Liouville theory \nby Remi Rhodes (Aix-Marseille Université) as part of MIT probabilit y seminar\n\nLecture held in Room 2 - 361 in the Simons Building.\n\nAbstr act\nConformal field theories (CFT) are expected to describe models of sta tistical physics in 2D undergoing a second order phase transition at their critical point. Several axiomatics have been proposed to lay the mathemat ical foundations for the concept of CFT. In Segal’s approach\, the data for a CFT are an Hilbert space H and a map that associates to each Rieman n surface S with boundary a Hilbert-Schmidt operator (called amplitude) ac ting on the tensor product $H^b$ with b the number of boundary components of S. Amplitudes are then assumed to compose in a natural way under gluing of surfaces along their boundaries. Segal’s approach turned out to be v ery attractive for mathematicians in view of its geometric flavor. Also\, it gives a geometrical way to understand the conformal bootstrap conjectur e in physics: correlation functions of CFT should factorize as an integral over their spectrum of the product of (squared) conformal blocks times th e structure constants of the CFT (the 3 point correlation functions on the Riemann sphere). Conformal blocks are holomorphic functions of the moduli of the space of Riemann surfaces with marked point\, which are universal in the sense that they only depend on the commutation relations of a given Lie algebra\, the Virasoro algebra. Structure constants are model depende nt. In this talk I will explain how this picture for CFTs drawn by Segal a pplies to Liouville theory (LCFT)\, which is a non rational conformal fie ld theory developed in the early 80s in physics to describe random Riem annian metrics on Riemann surfaces.\n LOCATION:https://stable.researchseminars.org/talk/Probability/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme Silva (University of Sao Paolo) DTSTART:20220912T201500Z DTEND:20220912T211500Z DTSTAMP:20260404T094122Z UID:Probability/54 DESCRIPTION:Title: Universality for a class of statistics of Hermitian random mat rices and the integro-differential Painlevé II equation.\nby Guilherm e Silva (University of Sao Paolo) as part of MIT probability seminar\n\n\n Abstract\nIt has been known since the 1990s that fluctuations of eigenvalu es of random matrices\, when appropriately scaled and in the sense of one- point distribution\, converge to the Airy2 point process in the large matr ix limit. In turn\, the latter can be described by the celebrated Tracy-Wi dom distribution.\n\nIn this talk we discuss recent findings of Ghosal and myself\, showing that certain statistics of eigenvalues also converge uni versality to appropriate statistics of the Airy2 point process\, interpola ting between a hard and soft edge of eigenvalues. Such found statistics co nnect also to the integro-differential Painlevé II equation\, in analogy with the celebrated Tracy-Widom connection between Painlevé II and the Ai ry2 process.\n LOCATION:https://stable.researchseminars.org/talk/Probability/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Mucciconi (University of Warwick) DTSTART:20220919T201500Z DTEND:20220919T211500Z DTSTAMP:20260404T094122Z UID:Probability/55 DESCRIPTION:Title: Title to be announced\nby Matteo Mucciconi (University of Warwick) as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Probability/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Hough (Stony Brook University) DTSTART:20221031T201500Z DTEND:20221031T211500Z DTSTAMP:20260404T094122Z UID:Probability/56 DESCRIPTION:Title: Covering systems of congruences\nby Robert Hough (Stony Br ook University) as part of MIT probability seminar\n\n\nAbstract\n\\noinde nt A distinct covering system of congruences is a list of congruences\n\\[ \na_i \\bmod m_i\, \\qquad i = 1\, 2\, ...\, k\n\\]\nwhose union is the in tegers. Erd\\H{o}s asked if the least modulus $m_1$ of a distinct coverin g system of congruences can be arbitrarily large (the minimum modulus prob lem for covering systems\, \\$ 1000 ) and if there exist distinct covering systems of congruences all of whose moduli are odd (the odd problem for c overing systems\, \\$ 25). I'll discuss my proof of a negative answer to the minimum modulus problem\, and a quantitative refinement with Pace Niel sen that proves that any distinct covering system of congruences has a mod ulus divisible by either 2 or 3. The proofs use the probabilistic method and in particular use a sequence of pseudorandom probability measures adap ted to the covering process. Time permitting\, I may briefly discuss a re formulation of our method due to Balister\, Bollob\\'{a}s\, Morris\, Sahas rabudhe and Tiba which solves a conjecture of Shinzel (any distinct coveri ng system of congruences has one modulus that divides another) and gives a negative answer to the square-free version of the odd problem.\n LOCATION:https://stable.researchseminars.org/talk/Probability/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandros Eskenazis (CNRS) DTSTART:20221003T201500Z DTEND:20221003T211500Z DTSTAMP:20260404T094122Z UID:Probability/57 DESCRIPTION:Title: Learning low-degree functions on the discrete hypercube\nb y Alexandros Eskenazis (CNRS) as part of MIT probability seminar\n\nLectur e held in Room 2-147 in the Simons Building.\n\nAbstract\nLet f be an unkn own function on the n-dimensional discrete hypercube. How many values of f do we need in order to approximately reconstruct the function? In this ta lk we shall discuss the random query model for this fundamental problem fr om computational learning theory. We will explain a newly discovered conne ction with a family of polynomial inequalities going back to Littlewood (1 930) which will in turn allow us to derive sharper estimates for the the q uery complexity of this model\, exponentially improving those which follow from the classical Low-Degree Algorithm of Linial\, Mansour and Nisan (19 89). Time permitting\, we will also show a matching information-theoretic lower bound. Based on joint works with Paata Ivanisvili (UC Irvine) and La uritz Streck (Cambridge).\n LOCATION:https://stable.researchseminars.org/talk/Probability/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Hao Shen (UW-Madison) DTSTART:20221024T201500Z DTEND:20221024T211500Z DTSTAMP:20260404T094122Z UID:Probability/58 DESCRIPTION:Title: Stochastic Yang-Mills process in 2D and 3D.\nby Hao Shen ( UW-Madison) as part of MIT probability seminar\n\nLecture held in Room 2-1 47 in the Simons Building.\n\nAbstract\nWe will discuss stochastic quantiz ation of the Yang-Mills model on two and three dimensional torus. In stoch astic quantization we consider the Langevin dynamic for the Yang-Mills mod el which is described by a stochastic PDE. We construct local solution to this SPDE and prove that the solution has a gauge invariant property in la w\, which then defines a Markov process on the space of gauge orbits. We w ill also describe the construction of this orbit space\, on which we have well-defined holonomies and Wilson loop observables. Based on joint work w ith Ajay Chandra\, Ilya Chevyrev\, and Martin Hairer.\n LOCATION:https://stable.researchseminars.org/talk/Probability/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Dor Elboim (Princeton University) DTSTART:20221107T211500Z DTEND:20221107T221500Z DTSTAMP:20260404T094122Z UID:Probability/59 DESCRIPTION:Title: Infinite cycles in the interchange process in five dimensions< /a>\nby Dor Elboim (Princeton University) as part of MIT probability semin ar\n\n\nAbstract\n\\noindent In the interchange process on a graph G=(V\,E )\, there is a particle on each vertex of the graph and an independent Poi sson clock on each one of the edges. Once the clock of an edge rings\, the two particles on the two sides of the edge switch. After time t\, the par ticles are permuted according to a random permutation $\\pi_t:V\\to V$. A famous conjecture of Balint Toth states that the following holds when $G=\ \mathbb$ $Z^d$ :\n(1) If d=2\, then the permutation $\\pi_t$ contains only finite cycles for all t>0.\n(2) If $d\\ge 3$\, then there exists $t_c$ su ch that for $tt_c$ \, $\\pi_t$ contains infinite cycles.\n\n\\vspace{2ex}\n\n\\noindent We pr ove the existence of infinite cycles for all $d\\ge 5$ and all $t$ suffici ently large. To this end\, we study the cyclic time random walk obtained b y exposing the cycle of the origin in $\\pi_t$. We show that this walk is diffusive using a multiscale inductive argument.\n\n\\vspace{2ex}\n\n\\noi ndent This is a joint work with Allan Sly.\n LOCATION:https://stable.researchseminars.org/talk/Probability/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Bailey (CUNY) DTSTART:20221121T211500Z DTEND:20221121T221500Z DTSTAMP:20260404T094122Z UID:Probability/60 DESCRIPTION:Title: Title to be announced\nby Emma Bailey (CUNY) as part of MI T probability seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Probability/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Hoi Nguyen (OSU) DTSTART:20221212T211500Z DTEND:20221212T221500Z DTSTAMP:20260404T094122Z UID:Probability/61 DESCRIPTION:Title: On roots of random trigonometric polynomials and related model s\nby Hoi Nguyen (OSU) as part of MIT probability seminar\n\nLecture h eld in Room 2-147 in the Simons Building.\n\nAbstract\nIn this talk we wil l discuss various basic statistics of the number of real roots of random t rigonometric polynomials\, as well as the minimum modulus and the nearest roots statistics to the unit circle of Kac polynomials. We emphasize the u niversality aspects of all these problems.\n\nBased on joint works with Co ok\, Do\, O. Nguyen\, Yakir and Zeitouni\n LOCATION:https://stable.researchseminars.org/talk/Probability/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Wang (MIT) DTSTART:20221114T211500Z DTEND:20221114T221500Z DTSTAMP:20260404T094122Z UID:Probability/62 DESCRIPTION:Title: Title to be announced\nby Sven Wang (MIT) as part of MIT p robability seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Probability/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Indigenous Peoples' Day (MIT) DTSTART:20221010T201500Z DTEND:20221010T211500Z DTSTAMP:20260404T094122Z UID:Probability/63 DESCRIPTION:Title: No Seminar On This Day\nby Indigenous Peoples' Day (MIT) a s part of MIT probability seminar\n\n\nAbstract\nhttps://news.mit.edu/2022 /indigenous-scholarship-mit-0425\n LOCATION:https://stable.researchseminars.org/talk/Probability/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Sayan Das DTSTART:20221128T211500Z DTEND:20221128T221500Z DTSTAMP:20260404T094122Z UID:Probability/64 DESCRIPTION:by Sayan Das as part of MIT probability seminar\n\nAbstract: T BA\n LOCATION:https://stable.researchseminars.org/talk/Probability/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Changji Xu DTSTART:20221205T211500Z DTEND:20221205T221500Z DTSTAMP:20260404T094122Z UID:Probability/65 DESCRIPTION:by Changji Xu as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Probability/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Remy (IAS\, Princeton) DTSTART:20221017T201500Z DTEND:20221017T211500Z DTSTAMP:20260404T094122Z UID:Probability/66 DESCRIPTION:Title: Modular transformation of conformal blocks via Liouville CFT\nby Guillaume Remy (IAS\, Princeton) as part of MIT probability seminar \n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\nConfor mal blocks are objects of fundamental importance in mathematical physics. They are a key input to the conformal bootstrap program to exactly solve 2 D conformal field theory (CFT) and are related to 4D supersymmetric gauge theory through the Alday-Gaiotto-Tachikawa correspondence. They are typica lly defined as power series via the representation theory of the Virasoro algebra but in this talk we will provide novel probabilistic expressions u sing the Gaussian free field. This will allow us to obtain many analytic p roperties such as modular transformations. Our methods are based on recent developments in the probabilistic construction of the Liouville CFT\, a t heory first introduced to describe random surfaces by A. Polyakov in the c ontext of string theory. Based on joint work with Promit Ghosal\, Xin Sun\ , and Yi Sun.​\n LOCATION:https://stable.researchseminars.org/talk/Probability/66/ END:VEVENT END:VCALENDAR