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