06/10/2021, 17:00 — 18:00 — Online
Marielle Simon, Inria, University of Lille
Hydrodynamic limit for a facilitated exclusion process
In this talk I will present 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. Several questions are still open, I will also give some research directions.
Based on joint works with O. Blondel, C. Erignoux and M. Sasada
