Call a Markov process "ergodic" if the following conditions hold: (a) The process has a unique invariant measure $\nu$. (b) If $\mu_0$ is any initial distribution for the process, then the resulting distribution $\mu_t$ at time $t$ will converge weakly to $\nu$ as $t \rightarrow \infty$. In this paper, necessary and sufficient conditions are obtained for the ergodicity of a certain infinite particle process. This process models a dissonant voting system, and is similar to one treated in Holley and Liggett (1975).
"Ergodicity Conditions for a Dissonant Voting Model." Ann. Probab. 5 (3) 371 - 386, June, 1977. https://doi.org/10.1214/aop/1176995798