The Annals of Probability
- Ann. Probab.
- Volume 3, Number 4 (1975), 643-663.
Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model
Richard A. Holley and Thomas M. Liggett
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 in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996306
Digital Object Identifier
doi:10.1214/aop/1176996306
Mathematical Reviews number (MathSciNet)
MR402985
Zentralblatt MATH identifier
0367.60115
JSTOR
links.jstor.org
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. Ann. Probab. 3 (1975), no. 4, 643--663. doi:10.1214/aop/1176996306. https://projecteuclid.org/euclid.aop/1176996306
