Recurrent random walk of an infinite particle system

Let p (x, y) be the transition function for a symmetric irreducible recurrent Markov chain on a countable set S. Let ₜ be the infinite particle system on S moving according to simple exclusion interaction with the one particle motion determined by p. Assume that p is such that any two particles moving independently on S will sooner or later meet. Then it is shown that every invariant measure for ₜ is a convex combination of Bernoulli product measures _ on \{ 0, 1\ ˢ} with density 0 = (x) = 1 1. Ergodic theorems are proved concerning the convergence of the system to one of the _.