## The Annals of Probability

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

### Ergodicity Conditions for a Dissonant Voting Model

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60J25: Continuous-time Markov processes on general state spaces

**Keywords**

Infinite particle system ergodic Markov process invariant measure

#### Citation

Matloff, Norman S. Ergodicity Conditions for a Dissonant Voting Model. Ann. Probab. 5 (1977), no. 3, 371--386. doi:10.1214/aop/1176995798. https://projecteuclid.org/euclid.aop/1176995798.