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:20260422T212608Z UID:PSA/1 DESCRIPTION:Title: The Mathematics of making a mess (an introduction to random walk on groups)\nby Persi Diaconis (Stanford University) as part of Probability and Stoc hastic Analysis at Tecnico Lisboa\n\n\nAbstract\nHow many random transposi tions does it take to mix up $n$ cards? This is a typical question of rand om walk on finite groups. The answer is $\\frac{1}{2}n \\log{n} + Cn$ and there is a sharp phase transition from order to chaos as $C$ varies. The t echniques involve Fourier analysis on non-commutative groups (which I will try to explain for non specialists). As you change the group or change th e walk\, new analytic and algebraic tools are required. The subject has wi de applications (people still shuffle cards\, but there are applications i n physics\, chemistry\,biology and computer science — even for random tr anspositions). Extending to compact or more general groups opens up many p roblems. This was the first problem where the ‘cutoff phenomenon’ was observed and this has become a healthy research area.\n LOCATION:https://researchseminars.org/talk/PSA/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Nina Gantert (Technische Universität München) DTSTART:20201110T140000Z DTEND:20201110T150000Z DTSTAMP:20260422T212608Z UID:PSA/2 DESCRIPTION:Title: Mixi ng times for the simple exclusion process with open boundaries\nby Nin a Gantert (Technische Universität München) as part of Probability and St ochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe study mixing times o f the symmetric and asymmetric simple exclusion process on the segment whe re particles are allowed to enter and exit at the endpoints. We consider d ifferent regimes depending on the entering and exiting rates as well as on the rates in the bulk\, and show that the process exhibits pre-cutoff and in some special cases even cutoff.\n LOCATION:https://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:20260422T212608Z UID:PSA/3 DESCRIPTION:Title: Stat ic large deviations for a reaction-diffusion model\nby Claudio Landim (Instituto Nacional de Matemática Pura e Aplicada (IMPA)) as part of Prob ability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe examin e the stationary state of an interacting particle system whose macroscopic evolution is described by one-dimensional reaction-diffusion equations.\n LOCATION:https://researchseminars.org/talk/PSA/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Serguei Popov (Universidade de Porto) DTSTART:20210112T140000Z DTEND:20210112T150000Z DTSTAMP:20260422T212608Z UID:PSA/4 DESCRIPTION:Title: Cond itioned SRW in two dimensions and some of its surprising properties\nb y Serguei Popov (Universidade de Porto) as part of Probability and Stochas tic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the two-dimensio nal simple random walk conditioned on never hitting the origin. This proce ss is a Markov chain\, namely it is the Doob $h$-transform of the simple r andom walk\nwith respect to the potential kernel. It is known to be transi ent and we show that it is "almost recurrent" in the sense that each infin ite set is visited infinitely often\, almost surely. After discussing some basic properties of this process (in particular\, calculating its Green's function)\, we prove that\, for a "large" set\, the proportion of its sit es visited by the conditioned walk is approximately a Uniform$[0\,1]$ rand om variable. Also\, given a set $G\\subset R^2$ that does not "surround" t he origin\, we prove that a.s. there is an infinite number of $k$'s such t hat $kG\\cap Z^2$ is unvisited. These results suggest that the range of th e conditioned walk has "fractal" behavior. Also\, we obtain estimates on t he speed of escape of the walk to infinity\, and prove that\, in spite of transience\, two independent copies of conditioned walks will a.s. meet in finitely many tim\n LOCATION:https://researchseminars.org/talk/PSA/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Tarrès (New York University Shanghai) DTSTART:20210209T140000Z DTEND:20210209T150000Z DTSTAMP:20260422T212608Z UID:PSA/5 DESCRIPTION:Title: Rein forced random walks and statistical physics\nby Pierre Tarrès (New Yo rk University Shanghai) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe explain how the Edge-reinforced random wa lk\, introduced by \nCoppersmith and Diaconis in 1986\, is related to seve ral models in \nstatistical physics\, namely the supersymmetric hyperbolic sigma model \nstudied by Disertori\, Spencer and Zirnbauer (2010)\, the r andom \nSchrödinger operator and Dynkin's isomorphism.\n\nWe also discuss recent non-reversible generalizations of the ERRW and the VRJP. Based on joint works (or work in progress) with C. Sabot\, X. Zeng\, T. Lupu\, M. D isertori and S. Baccalado.\n LOCATION:https://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:20260422T212608Z UID:PSA/6 DESCRIPTION:Title: Exac t solution of an integrable particle system\nby Cristian Giardinà (Un iversità degli Studi di Modena e Reggio Emilia) as part of Probability an d Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe consider the fam ily of boundary-driven models introduced in [FGK] and show they can be sol ved exactly\, i.e. the correlations functions and the non-equilibrium stea dy-state have a closed-form expression. \n\nThe solution relies on probabi listic arguments and techniques inspired by integrable systems. As in the context of bulk-driven systems (scaling to KPZ)\, it is obtained in two st eps: i) the introduction of a dual process\; ii) the solution of the dual dynamics by Bethe ansatz. \n\nFor boundary-driven systems\, a general by -product of duality is the existence of a direct mapping (a conjugation) b etween the generator of the non-equilibrium process and the generator of t he associated reversible equilibrium process. Macroscopically\, this mappi ng was observed years ago by Tailleur\, Kurchan and Lecomte in the context of the Macroscopic Fluctuation Theory.\n\n[FGK] R. Frassek\, C. Giardinà \, J. Kurchan\, Non-compact quantum spin chains as integrable stochastic p article processes\, Journal of Statistical Physics 180\, 366-397 (2020).\n \nZoom password: 958 0581 3232\n LOCATION:https://researchseminars.org/talk/PSA/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yinon Spinka (University of British Columbia) DTSTART:20210421T160000Z DTEND:20210421T170000Z DTSTAMP:20260422T212608Z UID:PSA/7 DESCRIPTION:Title: A ta le of two balloons\nby Yinon Spinka (University of British Columbia) a s part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstr act\nFrom each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch\, they pop and disappear. Will balloons r each the origin infinitely often or not? We answer this question for vario us underlying spaces. En route we find a new(ish) 0-1 law\, and generalize bounds on independent sets that are factors of IID on trees. Joint work w ith Omer Angel and Gourab Ray.\n LOCATION:https://researchseminars.org/talk/PSA/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Tal Orenshtein (WIAS\, TU-Berlin) DTSTART:20210519T160000Z DTEND:20210519T170000Z DTSTAMP:20260422T212608Z UID:PSA/8 DESCRIPTION:Title: Roug h walks in random environment\nby Tal Orenshtein (WIAS\, TU-Berlin) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstra ct\nRandom walks in random environment (RWRE) have been extensively studie d in the last half-century. Functional central limit theorems (FCLT) hold in some prototypical classes such the reversible and the ballistic ones. T he latter are treated using rather different techniques\; Kipnis-Varadhan' s theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballistic class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrators in a continuous manner. It typically provides a framework for pathwise soluti ons of ordinary and partial stochastic differential equations driven by a singular noise. In the talk we shall discuss FCLT for additive functionals of Markov processes and regenerative processes lifted to the rough path s pace. The limiting rough path has two levels. The first one is the Brownia n motion\, whereas in the second we see a new feature: it is the iterated integral of the Brownian motion perturbed by a deterministic linear functi on called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the limiting path. In addition\, the construction of new examples for SDE approximatio ns is an immediate application.\n\nBased on collaborations (some still in progress) with Johannes Bäumler\, Noam Berger\, Jean-Dominique Deuschel\, Olga Lopusanschi\, Nicolas Perkowski and Martin Slowik.\n\nReferences:\n\ n1) Additive functionals as rough paths\, with Jean-Dominique Deuschel and Nicolas Perkowski\, Ann. Probab. 49(3): 1450-1479 (May 2021). DOI: 10.121 4/20-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: 10.30757/ALEA .v18-34.\n\n3) Rough invariance principle for delayed regenerative process es\, arXiv:2101.05222.\n LOCATION:https://researchseminars.org/talk/PSA/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugene Speer (Rutgers University) DTSTART:20210526T160000Z DTEND:20210526T170000Z DTSTAMP:20260422T212608Z UID:PSA/9 DESCRIPTION:Title: Faci litated Exclusion Processes\nby Eugene Speer (Rutgers University) as p art of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract \nFacilitated exclusion processes are lattice gasses in which a particle w ith 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 one dimen sion\, for both discrete-time and continuous-time dynamics and with varyin g degrees of asymmetry. We address two questions: What are the possible tr anslation invariant stationary states? If the initial state is Bernoulli\, what is the final state? This is joint work with Arvind Ayyer\, Shelly Go ldstein\, and Joel Lebowitz.\n LOCATION:https://researchseminars.org/talk/PSA/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Marianna Russkikh (Massachusetts Institute of Technology) DTSTART:20210616T160000Z DTEND:20210616T170000Z DTSTAMP:20260422T212608Z UID:PSA/10 DESCRIPTION:Title: Loz enge tilings and the Gaussian free field on a cylinder\nby Marianna Ru sskikh (Massachusetts Institute of Technology) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstract\nWe discuss new result s on lozenge tilings on an infinite cylinder\, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of th e $q^{vol}$ measure\, corresponding to random cylindric partitions\, the h eight function converges to a deterministic limit shape and fluctuations a round it are given by the Gaussian free field in the conformal structure p redicted by the Kenyon-Okounkov conjecture. Under another variant\, corres ponding to an unrestricted tiling model on the cylinder\, the fluctuations are given by the same Gaussian free field with an additional discrete Gau ssian shift component. Fluctuations of the latter type have been previousl y conjectured by Gorin for tiling models on planar domains with holes. Thi s talk is based on joint work with Andrew Ahn and Roger Van Peski.\n LOCATION:https://researchseminars.org/talk/PSA/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Servet Martínez (Universidad de Chile) DTSTART:20210630T160000Z DTEND:20210630T170000Z DTSTAMP:20260422T212608Z UID:PSA/11 DESCRIPTION:Title: Dis crete-time evolution in recombination\nby Servet Martínez (Universida d de Chile) as part of Probability and Stochastic Analysis at Tecnico Lisb oa\n\n\nAbstract\nWe study the discrete-time evolution of a recombination transformation in population genetics acting on the set of measures on gen etic sequences. The evolution can be described by a Markov chain on the se t of partitions that converges to the finest partition. We describe the ge ometric decay rate to the limit and the quasi-stationary behavior when con ditioned that the chain has not hit the limit.\n LOCATION:https://researchseminars.org/talk/PSA/11/ END:VEVENT END:VCALENDAR