Hydrodynamic limit for an activated exclusion process

par Marielle Simon

jeudi 29 nov. 2018, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ, La Doua)

I will present a microscopic model in the family of conserved lattice gases (CLG). Its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. We prove that, in the active phase (i.e. for initial profiles smooth enough and uniformly larger than the critical density 1/2), the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to the class of fast diffusion equations. The first step in the proof is to show that the system typically reaches an ergodic component in subdiffusive time.

Joint work with O. Blondel, C. Erignoux and M. Sasada