The Annals of Probability

Convergence to Total Occupancy in an Infinite Particle System with Interactions

Thomas M. Liggett

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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.

Article information

Source
Ann. Probab., Volume 2, Number 6 (1974), 989-998.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996494

Digital Object Identifier
doi:10.1214/aop/1176996494

Mathematical Reviews number (MathSciNet)
MR362564

Zentralblatt MATH identifier
0295.60086

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 47A35: Ergodic theory [See also 28Dxx, 37Axx]

Keywords
Infinite particle systems simple exclusion model ergodic theorems

Citation

Liggett, Thomas M. Convergence to Total Occupancy in an Infinite Particle System with Interactions. Ann. Probab. 2 (1974), no. 6, 989--998. doi:10.1214/aop/1176996494. https://projecteuclid.org/euclid.aop/1176996494


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