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
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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