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A Characterization of the Invariant Measures for an Infinite Particle System with Interactions. II

Thomas M. Liggett
Transactions of the American Mathematical Society
Vol. 198 (Oct., 1974), pp. 201-213
DOI: 10.2307/1996755
Stable URL: http://www.jstor.org/stable/1996755
Page Count: 13
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A Characterization of the Invariant Measures for an Infinite Particle System with Interactions. II
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Abstract

Let p(x,y) be the transition function for a symmetric, irreducible Markov chain on the countable set S. Let η(t) be the infinite particle system on S with the simple exclusion interaction and one-particle motion determined by p. The present author and Spitzer have determined all of the invariant measures of η(t), and have obtained ergodic theorems for η(t), under two different sets of assumptions. In this paper, these problems are solved in the remaining case.

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