Mixing times for the simple exclusion process in ballistic random environment

TL;DR

This paper studies how quickly the exclusion process mixes in a random environment with ballistic behavior, revealing that the mixing time order differs from the single-particle case depending on the environment's support.

Contribution

It provides new insights into the mixing times of exclusion processes in ballistic random environments, especially highlighting differences from single-particle dynamics.

Findings

Mixing time order depends on the environment's support.

In nestling environments, mixing time differs from single-particle case.

Results apply to large segments with linearly many particles.

Abstract

We consider the exclusion process on segments of the integers in a site-dependent random environment. We assume to be in the ballistic regime in which a single particle has positive linear speed. Our goal is to study the mixing time of the exclusion process when the number of particles is linear in the size of the segment. We investigate the order of the mixing time depending on the support of the environment distribution. In particular, we prove for nestling environments that the order of the mixing time is different than in the case of a single particle.