Recurrent random walk of an infinite particle system

Author:
Frank Spitzer

Journal:
Trans. Amer. Math. Soc. **198** (1974), 191-199

MSC:
Primary 60K35

MathSciNet review:
0375533

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the transition function for a symmetric irreducible recurrent Markov chain on a countable set . Let be the infinite particle system on moving according to simple exclusion interaction with the one particle motion determined by . Assume that is such that any two particles moving independently on will sooner or later meet. Then it is shown that every invariant measure for is a convex combination of Bernoulli product measures on with density . Ergodic theorems are proved concerning the convergence of the system to one of the .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0375533-6

Keywords:
Infinite particle systems,
invariant measures,
random walk,
ergodic theorems

Article copyright:
© Copyright 1974
American Mathematical Society