“Hydrodynamic limit of simple exclusion processes on point processes with random conductances”
Lunedì 6 Marzo 2023, ore 16:00 - Aula 1BC45 e Zoom - Alessandra Faggionato (Università di Roma La Sapienza)
Abstract
We consider continuous-time random walks on a simple point process with random symmetric jump rates. The jump range can be unbounded. We assume some second-moment conditions and that the above randomness is left invariant by the action of the group $G = \mathbb{R}^d$ or $G = \mathbb{Z}^d$. We then add the site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits a hydrodynamic limit in path space. The hydrodynamic equation is non-random and governed by the effective homogenized matrix D of the single random walk, which can be degenerate. The proof relies both on particle duality and on stochastic homogenization for a single random walk. We then focus on specific examples, including the simple exclusion process on Delaunay triangulations.
