O Seminário de Probabilidade e Mecânica Estatística se reúne às quartas às 13h, horário de Brasília (16:00 UTC).

Data: 1/2/2023
Palestrante: Augusto Teixeira, IMPA.
Título: Title:Phase transition for percolation with axes-aligned defects.
Resumo: In this talk we will review a model that was first introduced by Jonasson, Mossel and Peres. Starting with the usual square lattice on Z^2, entire rows (respectively columns) of edges extending along the horizontal (respectively vertical) direction are removed independently at random. On the remaining thinned lattice, Bernoulli bond percolation is performed, giving rise to a percolation model with infinite range dependencies under the annealed law. In 2005, Hoffman solved the main conjecture around this model: proving that this percolation process indeed undergoes a nontrivial phase transition. In this talk, besides reviewing this surprisingly challenging problem, we will present a novel proof, which replaces the dynamic renormalization presented previously by a static version. This makes the proof easier to follow and to extend to other models. We finally present some remarks on the sharpness of Hoffman’s result as well as a list of interesting open problems that we believe can provide a renewed interest in this family of questions. This talk is based on a joint work with M. Hilário, M. Sá and R. Sanchis.

Data: 8/2/2023
Palestrante: Elena Kosygina, City University of New York
Título: Convergence and non-convergence of some self-interacting random walks to Brownian motion perturbed at extrema.
Resumo: Generalized Ray-Knight theorems for edge local times proved to be a very useful tool for studying the limiting behavior of several classes of self-interacting random walks (SIRWs) on integers. Examples include some reinforced random walks, excited random walks, rotor walks with defects. I shall describe two classes of SIRWs introduced and studied by Balint Toth (1996), asymptotically free and polynomially self-repelling SIRWs, and discuss new results which resolve an open question posed in Toth’s paper. We show that in the asymptotically free case the rescaled SIRWs converge to a perturbed Brownian motion (conjectured by Toth) while in the polynomially self-repelling case the convergence to the conjectured process fails in spite of the fact that generalized Ray-Knight theorems clearly identify the unique candidate in the class of all perturbed Brownian motions. This negative result was somewhat unexpected. The question whether there is convergence in the polynomially self-repelling case and, if yes, then how to describe the limiting process is open. This is joint work with Thomas Mountford, EPFL, and Jonathon Peterson, Purdue University.

Data: 15/2/2023
Palestrante: Eric Luçon, Université Paris Cité.
Título: How large is the mean-field framework ?
Resumo: The canonical framework for mean-field systems is to consider N particles (diffusions, or dynamics with jumps etc) that interact on the complete graph in a uniform way, the strength of interaction between two particles being of size 1/N. The behavior of the system is hence captured by the empirical measure of the system which converges as $N\to\infty$ to the solution of a nonlinear Fokker Planck equation. The motivation of this talk is simple: what can we say if one no longer interacts on the complete graph, i.e. one removes connections between particles ? if the graph is sufficiently close to the complete graph, one expects the same asymptotic behavior. We will address this question at the level of the LLN and fluctuations of the empirical measure of the system. This is based on joint works with G. Giacomin, S. Delattre, F. Coppini and C. Poquet.

Data: 1/3/2023
Palestrante: Alessandra Occelli, Université d'Angers.
Título: TBA.

Data: 8/3/2023
Palestrante: Jinho Baik, University of Michigan
Título: TBA.

Data: 15/3/2023
Palestrante: Linjie Zhao, Wuhan University.
Título: TBA.

Data: 12/4/2023
Palestrante: Timo Seppalainen, University of Wisconsin
Título: TBA.

Data: 31/5/2023
Palestrante: Sylvie Méléard, École Polytechnique
Título: TBA.

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Seminários anteriores

Data: 25/1/2023
Palestrante: Milton Jara, IMPA.
Título: Stein's method for Markovian martingales.

Data: 18/01/2023
Palestrante: Fabio Toninelli, Technical University of Vienna.
Título: An SPDE version of (W)ASEP in dimension d greater or equal to 2

Seminários de 2022

Seminários de 2021


  • IMPA
  • IST Lisboa
  • UBA
  • UFBA
  • UFMG
  • UFRJ
  • Unicamp
  • Universidade do Porto
  • USP

Comitê científico

  • Claudio Landim (IMPA)
  • Marielle Simon (GSSI and INRIA)
  • Pablo Ferrari (UBA)
  • Patrícia Gonçalves (IST)
  • Sunder Sethuraman (Arizona)