A Characterization of the Invariant Measures for an Infinite Particle System with Interactions

Abstract

Let $p(x,y)$ be the transition function for a symmetric, irreducible, transient 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. A characterization is obtained of all the invariant measures for ${\eta _t}$ in terms of the bounded functions on S which are harmonic with respect to $p(x,y)$. Ergodic theorems are proved concerning the convergence of the system to an invariant measure.