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December, 1974 Convergence to Total Occupancy in an Infinite Particle System with Interactions
Thomas M. Liggett
Ann. Probab. 2(6): 989-998 (December, 1974). DOI: 10.1214/aop/1176996494


Let $p(x, y)$ be the transition function for an irreducible, positive recurrent, reversible 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 principal result is that there are no nontrivial invariant measures for $\eta_t$ which concentrate on infinite configurations of particles on $S$. Furthermore, it is proved that if the system begins with an arbitrary infinite configuration, then it converges in probability to the configuration in which all sites are occupied.


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Thomas M. Liggett. "Convergence to Total Occupancy in an Infinite Particle System with Interactions." Ann. Probab. 2 (6) 989 - 998, December, 1974.


Published: December, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0295.60086
MathSciNet: MR362564
Digital Object Identifier: 10.1214/aop/1176996494

Primary: 60K35
Secondary: 47A35

Keywords: ergodic theorems , infinite particle systems , simple exclusion model

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 6 • December, 1974
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