## The Annals of Probability

### Ergodicity Conditions for a Dissonant Voting Model

Norman S. Matloff

#### Abstract

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).

#### Article information

Source
Ann. Probab. Volume 5, Number 3 (1977), 371-386.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995798

Digital Object Identifier
doi:10.1214/aop/1176995798

Mathematical Reviews number (MathSciNet)
MR445646

Zentralblatt MATH identifier
0364.60119

JSTOR