Open Access
Translator Disclaimer
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

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

Download 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

Information

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

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

Subjects:
Primary: 60K35
Secondary: 47A35

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

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.2 • No. 6 • December, 1974
Back to Top