BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sarai Hernandez (Technion) DTSTART:20200921T201500Z DTEND:20200921T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/1 DESCRIPTION:Title: Scaling limits of uniform spanning trees in three dimensions \nby Sarai Hernandez (Technion) as part of IUB Probability seminar\n\n Abstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Chaojie Yuan (Indiana University) DTSTART:20200928T201500Z DTEND:20200928T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/2 DESCRIPTION:Title: Low variance couplings for stochastic models of intracellula r processes with time-dependent rate functions\nby Chaojie Yuan (India na University) as part of IUB Probability seminar\n\n\nAbstract\nA number of coupling strategies are first presented for stochastically modeled bioc hemical processes with time-dependent parameters. In particular\, the stac ked coupling is introduced and is shown to provide an exceptionally low va riance between the generated paths. This coupling will be useful in the nu merical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. \n\nAnalytical results r elated to this coupling is then derived in the context of Parametric Sensi tivity Analysis. Such results are sparse\, and previous analysis utilizes a global Lipschitz assumption\, which is only applicable to a small percen tage of the models found in the literature. We will extend the analysis to allow for (1) Locally Lipschitz intensity functions\, and (2) time depend ence in the parameters. In particular\, binary systems\, a class of models that accounts for the vast majority of systems considered in the literatu re\, satisfy the assumptions of our theory. This is joint work with David Anderson.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Mykhaylo Shkolnikov (Princeton University) DTSTART:20201005T201500Z DTEND:20201005T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/3 DESCRIPTION:Title: The supercooled Stefan problem\nby Mykhaylo Shkolnikov ( Princeton University) as part of IUB Probability seminar\n\n\nAbstract\nTh e Stefan problem arising from the physics of supercooled liquids poses maj or mathematical challenges due to the presence of blow-ups\, including eve n the definition of solutions. I will explain how the problem can be refor mulated in probabilistic terms and how related particle system models lead to an appropriate notion of a solution. The solutions can be then studied by probabilistic techniques and a sharp description of the blow-ups can b e established. Based on joint works with Francois Delarue and Sergey Nadto chiy.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarai Hernandez Torres (Technion – Israel Institute of Technolog y) DTSTART:20201012T201500Z DTEND:20201012T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/4 DESCRIPTION:Title: Chase-escape with death\nby Sarai Hernandez Torres (Tech nion – Israel Institute of Technology) as part of IUB Probability semina r\n\n\nAbstract\nChase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites while blue particles overtak e adjacent red particles. We can think of this model as rabbits escaping f rom wolves pursuing them on an infinite graph. There are two phases for ch ase-escape. If the rabbits spread fast enough\, then both species coexist at any time. Otherwise\, the wolves eat all the rabbits in a finite time. This talk presents a modification of chase-escape where each rabbit has a random lifespan\, after which it dies. When the underlying graph is a d-ar y tree\, chase-escape with death exhibits a new phase where death benefits the survival of the rabbit population. We will understand the phase trans itions of this process through a connection between probability and analyt ic combinatorics. This is a joint work with Erin Beckman\, Keisha Cook\, N icole Eikmeier\, and Matthew Junge.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ching Wei Ho (Indiana University) DTSTART:20201109T211500Z DTEND:20201109T220500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/5 DESCRIPTION:Title: The eigenvalues of the sum of a Hermitian matrix and an imag inary multiple of the GUE\nby Ching Wei Ho (Indiana University) as par t of IUB Probability seminar\n\n\nAbstract\nIn 1955\, Wigner computed that the limiting eigenvalue distribution of the Gaussian unitary ensemble (GU E) is the semicircle law. Random matrix theory then has been under develop ment for decades\; remarkably\, in the 90s\, Voiculescu discovered that fr ee probability theory can be used to study random matrices. In this talk\, I will speak on my recent work with Brian Hall\, where we use free probab ility to compute the limiting eigenvalue distribution of the sum of a dete rministic Hermitian matrix and an imaginary multiple of a GUE. Unless the Hermitian matrix is a zero matrix\, this random matrix is almost surely no n-normal.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shuwen Lou (Loyola University) DTSTART:20201116T211500Z DTEND:20201116T220500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/6 DESCRIPTION:Title: Distorted Brownian motion on spaces with varying dimension\nby Shuwen Lou (Loyola University) as part of IUB Probability seminar\n \n\nAbstract\nWe introduce "distorted Brownian motion" (dBM) on a state sp ace with varying dimension. Roughly speaking\, the state space consists of two components: a 3-dimensional component and a 1-dimensional component. These two parts are joined together at the origin. The restriction of dBM on the 3-d component models a homopolymer with attractive potential at the origin. The restriction of dBM on the 1-d component can be any diffusion satisfying typical regularity conditions. We will discuss several properti es of such processes\, including whether they are transient/recurrent\, th e corresponding radial process\, characterization via h-transform\, and th eir density estimates.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Curien DTSTART:20201130T150000Z DTEND:20201130T160000Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/7 DESCRIPTION:Title: Unraveling parking on random trees via random graphs\nby Nicolas Curien as part of IUB Probability seminar\n\n\nAbstract\nImagine a plane tree together with a configuration of particles (cars) at each ver tex. Each car tries to park on its node\, and if the latter is occupied\, it moves downward towards the root trying to find an empty slot. When the underlying plane tree is a critical Galton--Watson conditioned to be large \, and when the car arrivals are i.i.d. on each vertex\, we observe a phas e transition:\n- when the density of cars is small enough\, all but a few manage to park safely\,\n- whereas when the density of cars is high enough \, a positive fraction of them do not manage to park and exit through the root of the tree.\nThe critical density is an explicit function of the fir st two moments of the offspring distribution and cars arrivals (C. & Héna rd 2019). We shall give a new point of view on this process by coupling it with the ubiquitous Erdös--Rényi random graph process. This enables us to fully understand the (dynamical) phase transition in the scaling limit by relating it to the multiplicative coalescent process.\nThe talk is base d on a joint work with Olivier Hénard and an ongoing project with Alice C ontat.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Timar DTSTART:20210322T201500Z DTEND:20210322T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/9 DESCRIPTION:Title: The Free Uniform Spanning Forest is disconnected in some vir tually free groups\, depending on the generating set\nby Adam Timar as part of IUB Probability seminar\n\n\nAbstract\nThe uniform measure on the set of all spanning trees of a finite graph is a classical object in prob ability. In an infinite graph\, one can take an exhaustion by finite subgr aphs\, with some boundary conditions\, and take the limit measure. The Fre e Uniform Spanning Forest (FUSF) is one of the natural limits\, but it is less understood than the wired version\, the WUSF. If we take a finitely g enerated group\, then several properties of WUSF and FUSF have been known to be independent of the chosen Cayley graph of the group. Lyons and Peres asked if the number of trees in the FUSF is such.\n\nIn a joint work with Gabor Pete we give two different Cayley graphs of the same group such tha t the FUSF is connected in one of them and it has infinitely many trees in the other. Furthermore\, since our example is a virtually free group\, we obtained a counterexample to the general expectation\, explicitly conject ured by Tang\, that such "tree-like" graphs would have connected FUSF. Sev eral open questions are inspired by the results. I will also present some preliminary results and conjectures on phase transition phenomena that hap pen if we put conductances on the edges of the underlying graph. These lat ter are joint work with Alexy\, Borbenyi and Imolay.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Muruhan Rathinam DTSTART:20210315T201500Z DTEND:20210315T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/10 DESCRIPTION:Title: Scaling limits for Random Walks on Graphs Embedded in the E uclidean Space : An Approach to Model and Predict Macroscale Transport \nby Muruhan Rathinam as part of IUB Probability seminar\n\n\nAbstract\nWe propose random walks on suitably defined graphs as a framework for finesc ale\nmodeling of particle motion in an obstructed environment. This motiva tes our\nstudy of a periodic\, directed and weighted graph embedded in a E uclidean space\nand the scaling limit of the associated continuous time ra ndom walk on the\ngraph's nodes which jumps along the graph's edges with j ump rates given by\nthe edge weights.\nWe show that a suitably scaled vers ion of the process converges to a linear\ndrift\, and the case of interest to us is that of null drift. In this case\, we\nshow that a suitably resc aled process converges weakly to\na Brownian motion. The diffusivity of th e limiting Brownian motion can be\ncomputed by solving a set of linear alg ebra problems. These linear algebra\nproblems are analogous to the unit-ce ll problems in the homogenization theory \nfor PDEs. In the case of revers ible rates\, we provide a variational\ncharacterization of the effective d iffusivity analogous to the case of\nhomogenization theory for the diffusi on PDE. This characterization makes use\nof vector calculus on graphs. \n \nWe also present some sufficient conditions for null drift that include c ertain\nsymmetries of the graph. Time permitting\, we discuss multiscale r andom walks\nwhere in some parts of the space the jump rates are much slow er (but non-zero).\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Damron (Georgia Institute of Technology) DTSTART:20210301T211500Z DTEND:20210301T220500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/11 DESCRIPTION:Title: Critical first-passage percolation in two dimensions\nb y Michael Damron (Georgia Institute of Technology) as part of IUB Probabil ity seminar\n\n\nAbstract\nIn 2d first-passage percolation (FPP)\, we plac e nonnegative i.i.d. weights (t_e) on the edges of Z^2 and study the induc ed weighted graph pseudometric T = T(x\,y). If we denote by p = P(t_e = 0) \, then there is a transition in the large-scale behavior of the model as p varies from 0 to 1. When p < 1/2\, T(0\,x) grows linearly in x\, and whe n p > 1/2\, it is stochastically bounded. The critical case\, where p = 1/ 2\, is more subtle\, and the sublinear growth of T(0\,x) depends on the be havior of the distribution function of t_e near zero. I will discuss my wo rk 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 th e triangular lattice and\, more recently (c) studies the growth of T(0\,x) in a dynamical version of the model\, where weights are resampled accordi ng to independent exponential clocks. These are joint works with J. Hanson \, D. Harper\, W.-K. Lam\, P. Tang\, and X. Wang.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawley DTSTART:20210426T201500Z DTEND:20210426T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/12 DESCRIPTION:Title: Extreme first passage times of normal and anomalous diffusi on\nby Sean Lawley as part of IUB Probability seminar\n\n\nAbstract\nW hy do 300 million sperm cells search for the oocyte in human fertilization when only a single sperm cell is necessary? Why do 1000 calcium ions ente r a dendritic spine when only two ions are necessary to activate the relev ant receptors? The seeming redundancy in these and other biological system s can be understood in terms of extreme first passage time (FPT) theory.\n \nWhile FPT theory is often used to estimate timescales in biology\, the o verwhelming majority of studies focus on the time it takes a given single searcher to find a target. However\, in many scenarios the more relevant t imescale is the FPT of the first searcher to find a target from a large gr oup of searchers. This fastest or extreme FPT depends on rare events and i s often orders of magnitude faster than the FPT of a given single searcher . In this talk\, we will explain recent results in extreme FPT theory and show how they modify traditional notions of diffusion timescales.\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Gonzalez-Casanova DTSTART:20210412T201500Z DTEND:20210412T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/13 DESCRIPTION:Title: From continuous state branching processes to coalescents\nby Adrian Gonzalez-Casanova as part of IUB Probability seminar\n\n\nAbs tract\nThe relation between these two important families of processes has been investigated in some cases. For example\, in a a renowned paper by se ven authors\, the $\\beta$-coalescents are obtained as a functional of tw o independent $\\alpha$-stable branching processes. Using Gillispie's samp ling method\, we find that an analogous relation holds for every Lambda co alescent. Furthermore\, functionals of independent CSBPs with different la ws lead to frequency processes of coalescents with selection\, mutation\, efficiency and more. This is a joint work in progress with Maria Emilia Ca ballero (UNAM) and Jose Luis Perez (CIMAT).\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Hughes DTSTART:20210517T201500Z DTEND:20210517T210500Z DTSTAMP:20260404T044248Z UID:ProbabilityIUB/14 DESCRIPTION:Title: New path properties for measure-valued Markov processes \nby Thomas Hughes as part of IUB Probability seminar\n\n\nAbstract\nAbstr act: I will discuss support and path properties for measure-valued Markov processes. My main focus will be some new results about the density of the (α\,d\,β)-superprocess\, a spatial branching model associated to an α- stable spatial motion in d dimensions and a (1+β)-stable branching mechan ism. These include (i) strict positivity of the density at a fixed time (f or certain values of α and β) and (ii) a classification of the measures which the density “charges” almost surely\, and of the measures which the density fails to charge with positive probability\, when conditioned o n survival. The duality between the superprocess and a fractional PDE is c entral to our method\, and I will discuss how the probabilistic statements above correspond to new results about solutions to the PDE. \n\nIf time p ermits\, I will also discuss work with Ed Perkins on super-Brownian motion \, and recent work-in-progress with Xiaowen Zhou on the Fleming-Viot model .\n LOCATION:https://stable.researchseminars.org/talk/ProbabilityIUB/14/ END:VEVENT END:VCALENDAR