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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A characterization of the invariant measures for an infinite particle system with interactions. II


Author: Thomas M. Liggett
Journal: Trans. Amer. Math. Soc. 198 (1974), 201-213
MSC: Primary 60K35
DOI: https://doi.org/10.1090/S0002-9947-1974-0375531-2
MathSciNet review: 0375531
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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 $ \eta (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 $ \eta (t)$, and have obtained ergodic theorems for $ \eta (t)$, under two different sets of assumptions. In this paper, these problems are solved in the remaining case.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0375531-2
Keywords: Infinite particle systems, invariant measures, ergodic theorems
Article copyright: © Copyright 1974 American Mathematical Society