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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A characterization of the invariant measures for an infinite particle system with interactions. II
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by Thomas M. Liggett
Trans. Amer. Math. Soc. 198 (1974), 201-213
DOI: https://doi.org/10.1090/S0002-9947-1974-0375531-2

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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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • 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