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.
Highlights
The exclusion process is one of the most studied examples of an interacting particle system. It can be described in the following way: Suppose that we are given a graph and a set of indistinguishable particles, which we initially place on distinct sites of the graph
A comprehensive introduction to mixing times can be found in the book of Levin, Peres and Wilmer [12] which treats the case of the simple exclusion process with constant transition rates
We present our main results on the mixing time of the simple exclusion process in a random environment
Summary
The exclusion process is one of the most studied examples of an interacting particle system. It can be described in the following way: Suppose that we are given a graph and a set of indistinguishable particles, which we initially place on distinct sites of the graph. For a general introduction to the exclusion process we refer to Liggett [14]. A comprehensive introduction to mixing times can be found in the book of Levin, Peres and Wilmer [12] which treats the case of the simple exclusion process with constant transition rates. We consider the case, where the transition rates of the simple exclusion process are chosen i.i.d. according to some fixed distribution
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