Programação

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

O link de zoom é atualizado semanalmente antes de uma sessão de seminário e é fornecido abaixo.
Se você se cadastrar na lista de discussão, receberá o link às segundas-feiras

Link de zoom: https://impa-br.zoom.us/j/95805813232?pwd=Rnd4TU9pUTRhQm5xa0Mvb0gxa0xDUT09
ID da reunião: 958 0581 3232

Por favor, desligue seus vídeos pessoais para reduzir a largura de banda usada! Se você está tendo problemas com o zoom, também pode acessar via transmissão ao vivo do Youtube no canal: youtube.com/spmes