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

Liggett, Thomas M.

doi:10.1090/S0002-9947-1974-0375531-2

A characterization of the invariant measures for an infinite particle system with interactions. II
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Trans. Amer. Math. Soc. 198 (1974), 201-213 Request permission

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.

References

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