BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ofer Zeitouni (Weizmann Institute of Science) DTSTART:20200420T113000Z DTEND:20200420T123000Z DTSTAMP:20260404T094802Z UID:HSPETDS/1 DESCRIPTION:Title: Stability and instability of spectrum for noisy perturbations of no n-Hermitian matrices\nby Ofer Zeitouni (Weizmann Institute of Science) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\nLecture held in 309.\n\nAbstract\nWe discuss the spectrum of h igh dimensional non-Hermitian matrices under small noisy perturbations. Th at spectrum can be extremely unstable\, as the maximal nilpotent matrix JN with JN(i\,j)=1 iff j=i+1 demonstrates. Numerical analysts studied worst case perturbations\, using the notion of pseudo-spectrum. Our focus is on finding the locus of most eigenvalues (limits of density of states)\, as w ell as studying stray eigenvalues ("outliers"). I will describe the backgr ound\, show some fun and intriguing simulations\, and present some theorem s and work in progress concerning eigenvectors. No background will be assu med. The talk is based on joint work with Anirban Basak\, Elliot Paquette\ , and Martin Vogel.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tal Orenshtein (TU Berlin\, Weierstrass Institute and Free Univers ity of Berlin) DTSTART:20200427T113000Z DTEND:20200427T123000Z DTSTAMP:20260404T094802Z UID:HSPETDS/2 DESCRIPTION:Title: Rough walks in random environment\nby Tal Orenshtein (TU Berlin \, Weierstrass Institute and Free University of Berlin) as part of Horowit z seminar on probability\, ergodic theory and dynamical systems\n\nLecture held in 309.\n\nAbstract\nRandom walks in random environment have been ex tensively studied in the last half-century and invariance principles are k nown to hold in various cases. We shall discuss recent contributions\, whe re the scaling limit is obtained in the rough path space for the lifted ra ndom walk. Except for the immediate application to stochastic differential equations\, this provides new information on the structure of the limitin g path - an enhanced Brownian motion with a linearly perturbed second leve l\, which is characterized in various ways. Time permitting\, we shall ela borate on the main tools to tackle these problems. Based on joint works wi th Olga Lopusanschi\, with Jean-Dominique Deuschel and Nicolas Perkowski a nd with Johaness Bäumler\, Noam Berger and Martin Slowik.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Garban (Université Lyon 1) DTSTART:20200504T113000Z DTEND:20200504T123000Z DTSTAMP:20260404T094802Z UID:HSPETDS/4 DESCRIPTION:Title: Kosterlitz-Thouless transition and statistical reconstruction of th e Gaussian free field\nby Christophe Garban (Université Lyon 1) as pa rt of Horowitz seminar on probability\, ergodic theory and dynamical syste ms\n\nLecture held in 309.\n\nAbstract\nThe Berezinskii-Kosterlitz-Thoules s transition (BKT transition) is a phase transition which occurs in dimens ion two for spin systems such as the plane rotator model (or XY model). Th is phase transition was discovered by these three physicists as the first example of a topological phase transition and was rigorously understood by Fröhlich and Spencer in the 80's. I will spend the main part of my talk explaining what are these topological phase transitions. I will then surve y the contributions of Fröhlich and Spencer to this theory and I will end with new results we obtained recently with Avelio Sepúlveda in this dire ction.\nThe talk will be based mostly on the preprint: https://arxiv.org/a bs/2002.12284\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Renan Gross (Weizmann Institute) DTSTART:20200511T113000Z DTEND:20200511T123000Z DTSTAMP:20260404T094802Z UID:HSPETDS/5 DESCRIPTION:Title: Stochastic processes for Boolean profit\nby Renan Gross (Weizma nn Institute) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\nLecture held in 309.\n\nAbstract\nNot even influe nce inequalities for Boolean functions can escape the long arm of stochast ic processes. I will present a (relatively) natural stochastic process whi ch turns Boolean functions and their derivatives into jump-process marting ales. There is much to profit from analyzing the individual paths of these processes: Using stopping times and level inequalities\, we will prove a conjecture of Talagrand relating edge boundaries and the influences\, and show stability of KKL\, isoperimetric\, and Talagrand's influence inequali ty. The technique (mostly) bypasses hypercontractivity. Work with Ronen El dan.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Izabella Stuhl (Penn State University) DTSTART:20200518T120000Z DTEND:20200518T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/6 DESCRIPTION:Title: The hard-core model in discrete 2D\nby Izabella Stuhl (Penn Sta te University) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nThe hard-core model describes a syst em of non-overlapping identical hard spheres in a space or on a lattice (m ore generally\, on a graph). An interesting open problem is: do hard disks in a plane admit a unique Gibbs measure at high density? It seems natural to approach this question by possible discrete approximations where disks must have the centers at sites of a lattice or vertices of a graph.\n\nIn this talk\, I will report on progress achieved for the models on a unit t riangular lattice $\\mathbb{A}_2$\, square lattice $\\mathbb{Z}^2$ and a h oneycomb graph $\\mathbb{H}_2$ for a general value of disk diameter $D$ (i n the Euclidean metric). We analyze the structure of Gibbs measures for la rge fugacities (i.e.\, high densities) by means of the Pirogov-Sinai theor y and its modifications. It connects extreme Gibbs measures with dominant ground states.\n\nOn $\\mathbb{A}_2$ we give a complete description of the set of extreme Gibbs measures\; the answer is provided in terms of the pr ime decomposition of the Löschian number $D^2$ in the Eisenstein integer ring. On $\\mathbb{Z}^2$\, we work with Gaussian numbers. Here we have to exclude a finite collection of values of $D$ with sliding\; for the remain ing exclusion distances the answer is given in terms of solutions to a dis crete minimization problem. The latter is connected to norm equations in t he cyclotomic integer ring $\\mathbb{Z}[\\zeta]$\, where $\\zeta$ is a pri mitive 12th root of unity. On $\\mathbb{H}_2$\, we employ connections with the model on $\\mathbb{A}_2$\, although there are some exceptional values requiring a special approach.\n\nParts of our argument contain computer-a ssisted proofs: identification of instances of sliding\, resolution of dom inance issues. This is a joint work with A. Mazel and Y. Suhov.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Dario (Tel Aviv University) DTSTART:20200525T120000Z DTEND:20200525T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/7 DESCRIPTION:Title: Large-scale behavior of the Villain model at low temperature in d = 3\nby Paul Dario (Tel Aviv University) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nIn this talk\, we will study the Villain rotator model in dimension three and pro ve that\, at low temperature\, the truncated two-point function of the mod el decays asymptotically like $|x|^{2-d}$\, with an algebraic rate of conv ergence. The argument starts from the observation that the asymptotic prop erties of the Villain model are related to the large-scale behavior of a v ector-valued random surface with uniformly elliptic and infinite range pot ential\, following the arguments of Fröhlich\, Spencer and Bauerschmidt. We will then see that this behavior can be studied quantitatively by combi ning two sets of tools: the Helffer-Sjöstrand PDE\, initially introduced by Naddaf and Spencer to identify the scaling limit of the discrete Ginzbu rg-Landau model\, and the techniques of the quantitative theory of stochas tic homogenization developed by Armstrong\, Kuusi and Mourrat. Joint work with Wei Wu.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ofir Gorodetsky (Tel Aviv University) DTSTART:20200316T123000Z DTEND:20200316T133000Z DTSTAMP:20260404T094802Z UID:HSPETDS/9 DESCRIPTION:Title: The anatomy of integers and Ewens permutations\nby Ofir Gorodet sky (Tel Aviv University) as part of Horowitz seminar on probability\, erg odic theory and dynamical systems\n\n\nAbstract\nWe will discuss an analog y between integers and permutations\, an analogy which goes back to works of Erdős and Kac and of Billingsley which we shall survey. Certain statis tics of the prime factors of a uniformly drawn integer (between $1$ and $x $) agree\, in the limit\, with similar statistics of the cycles of a unifo rmly drawn permutation from the symmetric group on $n$ elements. This anal ogy is beneficial to both number theory and probability theory\, as one ca n often prove new number-theoretical results by employing probabilistic id eas\, and vice versa.\nThe Ewens measure with parameter Θ\, first discove red in the context of population genetics\, is a non-uniform measure on pe rmutations. We will present an analogue of this measure on the integers\, and show how natural questions on the integers have answers which agree wi th analogous problems for the Ewens measure. For example\, the size of the prime factors of integers which are sums of two squares\, and the cycle l engths of permutations drawn according to the Ewens measure with parameter 1/2\, both converge to the Poisson-Dirichlet process with parameter 1/2. We will convey some of the ideas behind the proofs.\nJoint work with Dor E lboim.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Matan Seidel (Tel Aviv University) DTSTART:20200323T123000Z DTEND:20200323T133000Z DTSTAMP:20260404T094802Z UID:HSPETDS/10 DESCRIPTION:Title: Random walks on circle packings\nby Matan Seidel (Tel Aviv Uni versity) as part of Horowitz seminar on probability\, ergodic theory and d ynamical systems\n\n\nAbstract\nA circle packing is a canonical way of rep resenting a planar graph. There is a deep connection between the geometry of the circle packing and the probabilistic property of recurrence/transie nce of the simple random walk on the underlying graph\, as shown in the fa mous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However\, by usi ng certain natural weights that arise from the circle packing for a weight ed random walk\, (at least) one of the directions of the He-Schramm Theore m remains true. In the talk I will present some of the theory of circle pa ckings and random walks and discuss some of the ideas used in the proof. J oint work with Ori Gurel-Gurevich.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathanaël Berestycki (University of Vienna) DTSTART:20200330T113000Z DTEND:20200330T123000Z DTSTAMP:20260404T094802Z UID:HSPETDS/11 DESCRIPTION:Title: Random walks on random planar maps and Liouville Brownian motion\nby Nathanaël Berestycki (University of Vienna) as part of Horowitz se minar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\ nThe study of random walks on random planar maps was initiated in a series of seminal papers of Benjamini and Schramm at the end of the 90s\, motiva ted by contemporary (nonrigourous) works in the study of Liouville Quantum Gravity (LQG). Both topics have been the subject of intense research foll owing remarkable breakthroughs in the last few years.\n\nAfter reviewing s ome of the recent developments in these fields - including Liouville Brown ian motion\, a canonical notion of diffusion on LQG surfaces - I will desc ribe some joint work with Ewain Gwynne. In this work we show that random w alks on certain models of random planar maps (known as mated-CRT planar ma ps) have a scaling limit given by Liouville Brownian motion. This is true whether the maps are embedded using SLE/LQG theory or more intrinsically u sing the Tutte embedding. This is the first result confirming that Liouvil le Brownian motion is the scaling limit of random walks on random planar m aps.\n\nThe proof relies on some earlier work of Gwynne\, Miller and Sheff ield which proves convergence to Brownian motion\, modulo time-parametrisa tion. As an intermediate result of independent interest\, we derive an axi omatic characterisation of Liouville Brownian motion\, for which the notio n of Revuz measure of a Markov process plays a crucial role.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Chelkak (École Normale Supérieure Paris and St. Petersbur g Dept. of Steklov Institute RAS) DTSTART:20200601T120000Z DTEND:20200601T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/12 DESCRIPTION:Title: Bipartite dimer model: Gaussian Free Field on Lorentz-minimal surf aces\nby Dmitry Chelkak (École Normale Supérieure Paris and St. Pete rsburg Dept. of Steklov Institute RAS) as part of Horowitz seminar on prob ability\, ergodic theory and dynamical systems\n\n\nAbstract\nWe discuss a new viewpoint on the convergence of fluctuations in the bipartite dimer m odel considered on big planar graphs. Classically\, when these graphs are parts of refining lattices\, the boundary profile of the height function a nd a lattice-dependent entropy functional are responsible for the conforma l structure\, in which the limiting GFF (and CLE(4)) should be defined. Mo tivated by a long-term perspective of understanding the `discrete conforma l structure’ of random planar maps equipped with the dimer (or the criti cal Ising) model\, we introduce `perfect t-embeddings’ of abstract weigh ted bipartite graphs and argue that such embeddings reveal the conformal s tructure in a universal way: as that of a related Lorentz-minimal surface in 2+1 (or 2+2) dimensions.\n\nThough the whole concept is very new\, conc rete deterministic examples (e.g\, the Aztec diamond) justify its relevanc e\, and general convergence theorems obtained so far are of their own inte rest. Still\, many open questions remain\, one of the key ones being to un derstand the mechanism behind the appearance of the Lorentz metric in this classical problem.\n\nBased upon recent joint works with Benoît Laslier\ , Sanjay Ramassamy and Marianna Russkikh.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Bodineau (École Polytechnique) DTSTART:20200608T120000Z DTEND:20200608T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/13 DESCRIPTION:Title: Fluctuating Boltzmann equation and large deviations for a hard sph ere gas\nby Thierry Bodineau (École Polytechnique) as part of Horowit z seminar on probability\, ergodic theory and dynamical systems\n\n\nAbstr act\nSince the seminal work of Lanford\, the convergence of the hard-spher e dynamics towards the Boltzmann equation has been established in a dilute gas asymptotic. In this talk\, we are going to discuss the fluctuations o f this microscopic dynamics around the Boltzmann equation and the converge nce of the fluctuation field to a generalised Ornstein-Uhlenbeck process. We will show also that the occurrence of atypical evolutions can be quanti fied by a large deviation principle. This analysis relies on the study of the correlations created by the Hamiltonian dynamics. We will see that the emergence of irreversibility in the kinetic limit can be related to the s ingularity of these correlations.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Osama Khalil (University of Utah) DTSTART:20200615T140000Z DTEND:20200615T150000Z DTSTAMP:20260404T094802Z UID:HSPETDS/14 DESCRIPTION:Title: Singular Vectors on Fractals and Homogeneous Flows\nby Osama K halil (University of Utah) as part of Horowitz seminar on probability\, er godic theory and dynamical systems\n\n\nAbstract\nThe theory of Diophantin e approximation is underpinned by Dirichlet’s fundamental theorem. Broad ly speaking\, the main questions in the theory concern quantifying the pre valence of points with exceptional behavior with respect to Dirichlet’s result. The work of Dani and Kleinbock-Margulis connects these questions t o the recurrence behavior of certain flows on homogeneous spaces. For exam ple\, divergent orbits of such flows correspond to so-called singular vect ors. After a brief overview of the subject and the motivating questions\, I will discuss new results giving a sharp upper bound on the Hausdorff dim ension of divergent orbits of certain diagonal flows emanating from fracta ls on the space of unimodular lattices. Time permitting\, connections to t he theory of projections of self-similar measures will be presented.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Helmuth (University of Bristol) DTSTART:20200622T120000Z DTEND:20200622T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/15 DESCRIPTION:Title: Random spanning forests and hyperbolic symmetry\nby Tyler Helm uth (University of Bristol) as part of Horowitz seminar on probability\, e rgodic theory and dynamical systems\n\n\nAbstract\nThe arboreal gas is the probability measure that arises from conditioning the random subgraph giv en by Bernoulli($p$) bond percolation to be a spanning forest\, i.e.\, to contain no cycles. This conditioning makes sense on any finite graph $G$\, and in the case $p=1/2$ gives the uniform measure on spanning forests. Th e arboreal gas also arises as a $q\\to0$ limit of the $q$-state random clu ster model.\n\nWhat are the percolative properties of these forests? This turns out to be a surprisingly rich question\, and I will discuss what is known and conjectured. I will also describe a tool for studying connection probabilities\, the magic formula\, which arises due to an important conn ection between the arboreal gas and spin systems with hyperbolic symmetry. \n\nBased on joint work with Roland Bauerschmidt\, Nick Crawford\, and And rew Swan.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaar Solomon (Ben-Gurion university of the Negev) DTSTART:20200629T120000Z DTEND:20200629T130000Z DTSTAMP:20260404T094802Z UID:HSPETDS/16 DESCRIPTION:Title: Bounded-displacement non-equivalence in substitution tilings\n by Yaar Solomon (Ben-Gurion university of the Negev) as part of Horowitz s eminar on probability\, ergodic theory and dynamical systems\n\n\nAbstract \nGiven two Delone sets $Y$ and $Z$ in $R^d$ we study the existence of a b ounded-displacement (BD) map between them\, namely a bijection $f$ from $Y $ to $Z$ so that the quantity $\\|y-f(y)\\|$\, $y\\in Y$\, is bounded. Thi s notion induces an equivalence relation on collections $X$ of Delone sets and we study the cardinality of BD($X$)\, a collection of all BD-class re presentatives. In this talk we focus on sets $X$ of point sets that corres pond to tilings in a substitution tiling space. We provide a sufficient co ndition under which |BD($X$)| is the continuum. In particular we show that \, in the context of primitive substitution tilings\, |BD($X$)| can be gre ater than $1$.\n LOCATION:https://stable.researchseminars.org/talk/HSPETDS/16/ END:VEVENT END:VCALENDAR