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June, 1976 Coupling the Simple Exclusion Process
Thomas M. Liggett
Ann. Probab. 4(3): 339-356 (June, 1976). DOI: 10.1214/aop/1176996084


Consider the infinite particle system on the countable set $S$ with the simple exclusion interaction and one-particle motion determined by the stochastic transition matrix $p(x, y)$. In the past, the ergodic theory of this process has been treated successfully only when $p(x, y)$ is symmetric, in which case great simplifications occur. In this paper, coupling techniques are used to give a complete description of the set of invariant measures for the system in the following three cases: (a) $p(x, y)$ is translation invariant on the integers and has mean zero, (b) $p(x, y)$ corresponds to a birth and death chain on the nonnegative integers, and (c) $p(x, y)$ corresponds to the asymmetric simple random walk on the integers.


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Thomas M. Liggett. "Coupling the Simple Exclusion Process." Ann. Probab. 4 (3) 339 - 356, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0339.60091
MathSciNet: MR418291
Digital Object Identifier: 10.1214/aop/1176996084

Primary: 60K35

Keywords: coupling , Infinite particle system , Invariant measures , simple exclusion process

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
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