The Annals of Probability

Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model

Richard A. Holley and Thomas M. Liggett

Full-text: Open access

Abstract

A theorem exhibiting the duality between certain infinite systems of interacting stochastic processes and a type of branching process is proved. This duality is then used to study the ergodic properties of the infinite system. In the case of the vector model a complete understanding of the ergodic behavior is obtained.

Article information

Source
Ann. Probab. Volume 3, Number 4 (1975), 643-663.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176996306

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176996306

Mathematical Reviews number (MathSciNet)
MR402985

Zentralblatt MATH identifier
0367.60115

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Infinite particle system ergodic theorem branching process with interference Markov chain harmonic function

Citation

Holley, Richard A.; Liggett, Thomas M. Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model. The Annals of Probability 3 (1975), no. 4, 643--663. doi:10.1214/aop/1176996306. http://projecteuclid.org/euclid.aop/1176996306.


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