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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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Recurrent random walk of an infinite particle system
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by Frank Spitzer
Trans. Amer. Math. Soc. 198 (1974), 191-199
DOI: https://doi.org/10.1090/S0002-9947-1974-0375533-6

Abstract:

Let $p(x,y)$ be the transition function for a symmetric irreducible recurrent Markov chain on a countable set $S$. Let ${\eta _t}$ be the infinite particle system on $S$ moving according to simple exclusion interaction with the one particle motion determined by $p$. Assume that $p$ is such that any two particles moving independently on $S$ will sooner or later meet. Then it is shown that every invariant measure for ${\eta _t}$ is a convex combination of Bernoulli product measures ${\mu _\alpha }$ on ${\{ 0,1\} ^s}$ with density $0 \leqslant \alpha = \mu [\eta (x) = 1] \leqslant 1$. Ergodic theorems are proved concerning the convergence of the system to one of the ${\mu _\alpha }$.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 198 (1974), 191-199
  • MSC: Primary 60K35
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0375533-6
  • MathSciNet review: 0375533