Dear colleagues,
I would like to announce the following online seminar organized by the Probability group of the University of Pisa. The talks will be accessible under the link
Join Microsoft Teams Meetinghttps://teams.microsoft.com/l/meetup-join/19%3a17115d7f6ef44c5e91974362906cfc95%40thread.tacv2/1602238992289?context=%7b%22Tid%22%3a%22c7456b31-a220-47f5-be52-473828670aa1%22%2c%22Oid%22%3a%22dfd1e5f6-331d-43e0-a180-4bb6ce727fb7%22%7d https://aka.ms/JoinTeamsMeeting
Best regards,
Giacomo
https://aka.ms/JoinTeamsMeeting
Tuesday, Oct. 13, 14:00
Speaker: Mauro Mariani
Title: Quasi-invariant measures for a model of evolutionary biology
Abstract: I will discuss a class of random models for the genetic
evolution of a population of individuals with asexual reproduction.
Formally, this is a diffusion process on an infinite-dimensional
simplex. subject to absorption. It has been largely investigated in
the past, both numerically and analytically as a model for the
Muller's ratchet. We prove the existence and uniqueness of
quasi-invariant measures describing the long-time behavior of the
genetic distribution of the population, conditioned to non-extinction.
The seminar is mostly based on https://arxiv.org/abs/2007.14715
Tuesday, Oct. 13, 15:00
Speaker: Marielle Simon
Title: Hydrodynamic limit for a facilitated exclusion process
Abstract: In this talk we will be interested in a one-dimensional exclusion process subject to strong kinetic constraints, which belongs to the class of cooperative kinetically constrained lattice gases. More precisely, its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. We will see that the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to free boundary problems (or Stefan problems). One of the ingredients is to show that the system typically reaches an ergodic component in subdiffusive time.
Based on joint works with O. Blondel, C. Erignoux and M. Sasada