BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Persi Diaconis (Stanford University) DTSTART:20201013T130000Z DTEND:20201013T140000Z DTSTAMP:20260404T094503Z UID:PSA/1 DESCRIPTION:Title: The Mathematics of making a mess (an introduction to random walk on gro ups)\nby Persi Diaconis (Stanford University) as part of Probability a nd Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nHow many random tr anspositions does it take to mix up $n$ cards? This is a typical question of random walk on finite groups. The answer is $\\frac{1}{2}n \\log{n} + C n$ and there is a sharp phase transition from order to chaos as $C$ varies . The techniques involve Fourier analysis on non-commutative groups (which I will try to explain for non specialists). As you change the group or ch ange the walk\, new analytic and algebraic tools are required. The subject has wide applications (people still shuffle cards\, but there are applica tions in physics\, chemistry\,biology and computer science — even for ra ndom transpositions). Extending to compact or more general groups opens up many problems. This was the first problem where the ‘cutoff phenomenon ’ was observed and this has become a healthy research area.\n LOCATION:https://stable.researchseminars.org/talk/PSA/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Nina Gantert (Technische Universität München) DTSTART:20201110T140000Z DTEND:20201110T150000Z DTSTAMP:20260404T094503Z UID:PSA/2 DESCRIPTION:Title: Mixing times for the simple exclusion process with open boundaries\ nby Nina Gantert (Technische Universität München) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe study mixing times of the symmetric and asymmetric simple exclusion process on the segm ent where particles are allowed to enter and exit at the endpoints. We con sider different regimes depending on the entering and exiting rates as wel l as on the rates in the bulk\, and show that the process exhibits pre-cut off and in some special cases even cutoff.\n LOCATION:https://stable.researchseminars.org/talk/PSA/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Landim (Instituto Nacional de Matemática Pura e Aplicada (IMPA)) DTSTART:20201215T140000Z DTEND:20201215T150000Z DTSTAMP:20260404T094503Z UID:PSA/3 DESCRIPTION:Title: Static large deviations for a reaction-diffusion model\nby Claudio Landim (Instituto Nacional de Matemática Pura e Aplicada (IMPA)) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe examine the stationary state of an interacting particle system whose macr oscopic evolution is described by one-dimensional reaction-diffusion equat ions.\n LOCATION:https://stable.researchseminars.org/talk/PSA/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Serguei Popov (Universidade de Porto) DTSTART:20210112T140000Z DTEND:20210112T150000Z DTSTAMP:20260404T094503Z UID:PSA/4 DESCRIPTION:Title: Conditioned SRW in two dimensions and some of its surprising properties \nby Serguei Popov (Universidade de Porto) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the two-d imensional simple random walk conditioned on never hitting the origin. Thi s process is a Markov chain\, namely it is the Doob $h$-transform of the s imple random walk\nwith respect to the potential kernel. It is known to be transient and we show that it is "almost recurrent" in the sense that eac h infinite set is visited infinitely often\, almost surely. After discussi ng some basic properties of this process (in particular\, calculating its Green's function)\, we prove that\, for a "large" set\, the proportion of its sites visited by the conditioned walk is approximately a Uniform$[0\,1 ]$ random variable. Also\, given a set $G\\subset R^2$ that does not "surr ound" the origin\, we prove that a.s. there is an infinite number of $k$'s such that $kG\\cap Z^2$ is unvisited. These results suggest that the rang e of the conditioned walk has "fractal" behavior. Also\, we obtain estimat es on the speed of escape of the walk to infinity\, and prove that\, in sp ite of transience\, two independent copies of conditioned walks will a.s. meet infinitely many tim\n LOCATION:https://stable.researchseminars.org/talk/PSA/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Tarrès (New York University Shanghai) DTSTART:20210209T140000Z DTEND:20210209T150000Z DTSTAMP:20260404T094503Z UID:PSA/5 DESCRIPTION:Title: Reinforced random walks and statistical physics\nby Pierre Tarrès (New York University Shanghai) as part of Probability and Stochastic Analy sis at Tecnico Lisboa\n\n\nAbstract\nWe explain how the Edge-reinforced ra ndom walk\, introduced by \nCoppersmith and Diaconis in 1986\, is related to several models in \nstatistical physics\, namely the supersymmetric hyp erbolic sigma model \nstudied by Disertori\, Spencer and Zirnbauer (2010)\ , the random \nSchrödinger operator and Dynkin's isomorphism.\n\nWe also discuss recent non-reversible generalizations of the ERRW and the VRJP. Ba sed on joint works (or work in progress) with C. Sabot\, X. Zeng\, T. Lupu \, M. Disertori and S. Baccalado.\n LOCATION:https://stable.researchseminars.org/talk/PSA/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristian Giardinà (Università degli Studi di Modena e Reggio Emi lia) DTSTART:20210317T170000Z DTEND:20210317T180000Z DTSTAMP:20260404T094503Z UID:PSA/6 DESCRIPTION:Title: Exact solution of an integrable particle system\nby Cristian Giardi nà (Università degli Studi di Modena e Reggio Emilia) as part of Probabi lity and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the family of boundary-driven models introduced in [FGK] and show they can be solved exactly\, i.e. the correlations functions and the non-equilibri um steady-state have a closed-form expression. \n\nThe solution relies on probabilistic arguments and techniques inspired by integrable systems. As in the context of bulk-driven systems (scaling to KPZ)\, it is obtained in two steps: i) the introduction of a dual process\; ii) the solution of t he dual dynamics by Bethe ansatz. \n\nFor boundary-driven systems\, a gen eral by-product of duality is the existence of a direct mapping (a conjuga tion) between the generator of the non-equilibrium process and the generat or of the associated reversible equilibrium process. Macroscopically\, thi s mapping was observed years ago by Tailleur\, Kurchan and Lecomte in the context of the Macroscopic Fluctuation Theory.\n\n[FGK] R. Frassek\, C. Gi ardinà\, J. Kurchan\, Non-compact quantum spin chains as integrable stoch astic particle processes\, Journal of Statistical Physics 180\, 366-397 (2 020).\n\nZoom password: 958 0581 3232\n LOCATION:https://stable.researchseminars.org/talk/PSA/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yinon Spinka (University of British Columbia) DTSTART:20210421T160000Z DTEND:20210421T170000Z DTSTAMP:20260404T094503Z UID:PSA/7 DESCRIPTION:Title: A tale of two balloons\nby Yinon Spinka (University of British Colu mbia) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n \nAbstract\nFrom each point of a Poisson point process start growing a bal loon at rate 1. When two balloons touch\, they pop and disappear. Will bal loons reach the origin infinitely often or not? We answer this question fo r various underlying spaces. En route we find a new(ish) 0-1 law\, and gen eralize bounds on independent sets that are factors of IID on trees. Joint work with Omer Angel and Gourab Ray.\n LOCATION:https://stable.researchseminars.org/talk/PSA/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Tal Orenshtein (WIAS\, TU-Berlin) DTSTART:20210519T160000Z DTEND:20210519T170000Z DTSTAMP:20260404T094503Z UID:PSA/8 DESCRIPTION:Title: Rough walks in random environment\nby Tal Orenshtein (WIAS\, TU-Ber lin) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\ nAbstract\nRandom walks in random environment (RWRE) have been extensively studied in the last half-century. Functional central limit theorems (FCLT ) hold in some prototypical classes such the reversible and the ballistic ones. The latter are treated using rather different techniques\; Kipnis-Va radhan's theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballisti c class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrat ors in a continuous manner. It typically provides a framework for pathwise solutions of ordinary and partial stochastic differential equations drive n by a singular noise. In the talk we shall discuss FCLT for additive func tionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels. The first one is the Brownian motion\, whereas in the second we see a new feature: it is the it erated integral of the Brownian motion perturbed by a deterministic linear function called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the l imiting path. In addition\, the construction of new examples for SDE appro ximations is an immediate application.\n\nBased on collaborations (some st ill in progress) with Johannes Bäumler\, Noam Berger\, Jean-Dominique Deu schel\, Olga Lopusanschi\, Nicolas Perkowski and Martin Slowik.\n\nReferen ces:\n\n1) Additive functionals as rough paths\, with Jean-Dominique Deusc hel and Nicolas Perkowski\, Ann. Probab. 49(3): 1450-1479 (May 2021). DOI: 10.1214/20-AOP1488.\n\n2) Ballistic random walks in random environment as rough paths: convergence and area anomaly\, with Olga Lopusanschi\, ALEA \, Lat. Am. J. Probab. Math. Stat. 18\, 945–962 (April 2021) DOI: 10.307 57/ALEA.v18-34.\n\n3) Rough invariance principle for delayed regenerative processes\, arXiv:2101.05222.\n LOCATION:https://stable.researchseminars.org/talk/PSA/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugene Speer (Rutgers University) DTSTART:20210526T160000Z DTEND:20210526T170000Z DTSTAMP:20260404T094503Z UID:PSA/9 DESCRIPTION:Title: Facilitated Exclusion Processes\nby Eugene Speer (Rutgers Universit y) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nA bstract\nFacilitated exclusion processes are lattice gasses in which a par ticle with an empty neighboring site can jump to that site only if it has also an occupied neighboring site. We will discuss three such models in on e dimension\, for both discrete-time and continuous-time dynamics and with varying degrees of asymmetry. We address two questions: What are the poss ible translation invariant stationary states? If the initial state is Bern oulli\, what is the final state? This is joint work with Arvind Ayyer\, Sh elly Goldstein\, and Joel Lebowitz.\n LOCATION:https://stable.researchseminars.org/talk/PSA/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Marianna Russkikh (Massachusetts Institute of Technology) DTSTART:20210616T160000Z DTEND:20210616T170000Z DTSTAMP:20260404T094503Z UID:PSA/10 DESCRIPTION:Title: Lozenge tilings and the Gaussian free field on a cylinder\nby Mari anna Russkikh (Massachusetts Institute of Technology) as part of Probabili ty and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe discuss new results on lozenge tilings on an infinite cylinder\, which may be analyze d using the periodic Schur process introduced by Borodin. Under one varian t of the $q^{vol}$ measure\, corresponding to random cylindric partitions\ , the height function converges to a deterministic limit shape and fluctua tions around it are given by the Gaussian free field in the conformal stru cture predicted by the Kenyon-Okounkov conjecture. Under another variant\, corresponding to an unrestricted tiling model on the cylinder\, the fluct uations are given by the same Gaussian free field with an additional discr ete Gaussian shift component. Fluctuations of the latter type have been pr eviously conjectured by Gorin for tiling models on planar domains with hol es. This talk is based on joint work with Andrew Ahn and Roger Van Peski.\ n LOCATION:https://stable.researchseminars.org/talk/PSA/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Servet Martínez (Universidad de Chile) DTSTART:20210630T160000Z DTEND:20210630T170000Z DTSTAMP:20260404T094503Z UID:PSA/11 DESCRIPTION:Title: Discrete-time evolution in recombination\nby Servet Martínez (Uni versidad de Chile) as part of Probability and Stochastic Analysis at Tecni co Lisboa\n\n\nAbstract\nWe study the discrete-time evolution of a recombi nation transformation in population genetics acting on the set of measures on genetic sequences. The evolution can be described by a Markov chain on the set of partitions that converges to the finest partition. We describe the geometric decay rate to the limit and the quasi-stationary behavior w hen conditioned that the chain has not hit the limit.\n LOCATION:https://stable.researchseminars.org/talk/PSA/11/ END:VEVENT END:VCALENDAR