Perturbations of the Symmetric Exclusion Process

#### P. Jung

2004, v.10, Issue 4, 565-584

ABSTRACT

This paper gives results concerning the asymptotics of the invariant measures, $\mathcal{I},$ for exclusion processes where $p(x,y)=p(y,x)$ except for finitely many $x,y\in\mathcal{S}$ and $p(x,y)$ corresponds to a transient Markov chain on $\mathcal{S}$. As a consequence, a complete characterization of $\mathcal{I}$ is given for the case where $p(x,y)=p(y,x)$ for all but a single ordered pair $(u,v)$. Also, this paper addresses the question: When do local changes to a symmetric kernel $p(x,y)=p(y,x)$ affect the evolution of the exclusion process globally?

Keywords: interacting particle system,exclusion process,infinitesimal coupling,invariant measures