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

Data: 31/5/2023
Palestrante: Sylvie Méléard, École Polytechnique
Título: Exponent dynamics for branching processes.
Resumo: We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values on a grid of [0,1] with mutation and selection. Our aim is the study of the dynamics of the population in logarithm size and time scales, under a large population assumption.
In the first part of the talk, individual mutations are rare but the global mutation rate tends to infinity. Then negligible sub-populations may have a strong contribution to evolution. The traits can also be horizontally transferred, leading to a trade-off between natural evolution to higher birth rates and transfer which drives the population towards lower birth rates. We prove that the stochastic discrete exponent process converges to a piecewise affine continuous function, which can be described along successive phases determined by dominant traits.
In the second part of the talk, the individual mutations are small but not rare, we don’t have transfer and we assume the grid mesh for the trait values becoming smaller and smaller. Here again, the contribution of small sub-populations is important. We establish that under our rescaling, the stochastic discrete exponent process converges to the viscosity solution of a Hamilton-Jacobi equation, filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations.
Joint works with N. Champagnat and V.C. Tran, and S. Mirrahimi for the second part.

Data: 07/06/2023
Palestrante: Clement Erignoux, INRIA, Lille
Título: Modelling active matter by active lattice gases : exact hydrodynamic description and phase transitions.
Resumo: In this talk, I will introduce a few related microscopic models for active matter. The models we consider are lattice gases, meaning that the active particles jump stochastically on a lattice. Their active nature is represented by a drift in their stochastic jumps, whose direction can evolve in time as particles interact with eachother. I will discuss how, with this type of lattice gases, one can model the behavior of active matter, and recover the emergence of Vicsek's alignment phase transition as well as Motility Induced Phase Separation (MIPS), both classical phenomena for active matter. Both have been well documented by the physics community, however mathematical results remain scarce. Notably, using the mathematical theory of hydrodynamic limit, one can prove the emergence of both phenomena mathematically, even for models with purely local interactions, without any mean-field type assumptions. I will talk about recent results on phase separation occuring in a non gradient active gas, and how even small proportion of active particles can induce phase separation.Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with binary collisions and show that these solutions are atypical. More precisely, we prove that the probability of observing these paths is exponentially small in the number of particles and compute the exponential rate. Based on JW with Mourtaza Kourbane Houssène, Julien Tailleur, Thierry Bodineau, James Mason, Maria Bruna, Robert Jack

Data: 14/6/2023
Palestrante: Partha Dey, University of Illinois, Urbana-Champaign
Título: TBA.

Data: 21/6/2023
Palestrante: Assaf Shapira, Université Paris Cité
Título: TBA
Resumo: TBA

Data: 5/7/2023
Palestrante: Alessandra Occelli, Université d'Angers
Título: TBA
Resumo: TBA

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Seminários anteriores

Data: 24/5/2023
Palestrante: Lorenzo Bertini, La Sapienza, Roma
Título: On the probability of observing energy increasing solutions to the Boltzmann equation.

Data: 17/5/2023
Palestrante: Alex Dunlap, New York University
Título: The nonlinear stochastic heat equation in the critical dimension

Data: 10/5/2023
Palestrante: Kevin Yang, UC Berkeley
Título: Universality and well-posedness for a time-inhomogeneous KPZ equation

Data: 3/5/2023
Palestrante: Federico Sau, University of Trieste
Título: Spectral gap of the symmetric inclusion proces

Data: 26/4/2023
Palestrante: Fraydoun Rezakhanlou, Berkeley
Título: Kinetic Theory for Laguerre Tessellations

Data: 19/4/2023
Palestrante: Giuseppe Cannizzaro, University of Warwick and UKRI Future Leaders Fellow.
Título: Title: Weak coupling scaling of critical SPDES.

Data: 12/4/2023
Palestrante: Timo Seppalainen, University of Wisconsin
Título: Stationary horizon as the universal multitype stationary distribution Video

Data: 05/4/2023
Palestrante: Chiara Franceschini, University of Modena
Título: Two duality relations for Markov processes with an open boundary

Data: 29/3/2023
Palestrante: Stefan Grosskinsky, Augsburg
Título: Size-biased diffusion limits for the inclusion process

Data: 22/3/2023
Palestrante: Benoit Dagallier, Cambridge, UK
Título: Large deviations for out of equilibrium correlations in the symmetric simple exclusion process. Video

Data: 15/3/2023
Palestrante: Linjie Zhao, Wuhan University.
Título: The tagged particle in asymmetric exclusion process with long jumps. Video

Data: 8/3/2023
Palestrante: Jinho Baik, University of Michigan
Título: Multi-point distribution of periodic TASEP and differential equations. Video

Data: 1/3/2023
Palestrante: Mario Ayala, Technische Universität München (TUM).
Título: Fluctuation fields and orthogonal self-dualities.

Data: 22/2/2023
Palestrante: Minmin Wang, University of Sussex.
Título: Geometry of a large random intersection graph inside the critical window

Data: 15/2/2023
Palestrante: Eric Luçon, Université Paris Cité.
Título: How large is the mean-field framework ?

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.

Data: 1/2/2023
Palestrante: Augusto Teixeira, IMPA.
Título: Phase transition for percolation with axes-aligned defects.

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)