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

Best regards, 

Giacomo 

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