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Extremal reversible measures for the exclusion process. (English) Zbl 1025.60045
Author’s summary: 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 proves information concerning the domains of attraction for reversible measures.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics
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