Extremal Reversible Measures for the Exclusion Process

Abstract

The invariant measures \({\mathcal{I}}\) for the exclusion process have long been studied and a complete description is known in many cases. This paper gives characterizations of \({\mathcal{I}}\) for exclusion processes on \({\mathbb{Z}}\) with certain reversible transition kernels. Some examples for which \({\mathcal{I}}\) is given include all finite range kernels that are asymptotically equal to p(x,x+1)=p(x,x−1)=1/2. One tool used in the proofs gives a necessary and sufficient condition for reversible measures to be extremal in the set of invariant measures, which is an interesting result in its own right. One reason that this extremality is interesting is that it provides information concerning the domains of attraction for reversible measures.

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Jung, P. Extremal Reversible Measures for the Exclusion Process. Journal of Statistical Physics 112, 165–191 (2003). https://doi.org/10.1023/A:1023679620839

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  • exclusion process
  • invariant measures
  • extremal invariant measures
  • domains of attraction