Abstract
We examine a one-dimensional class of interacting particle systems which generalize some voter models. This class includes a particular case in the class of models of catalytic surfaces introduced by Swindle and Grannan. We show that this class has the “clustering” property of ordinary finite-range voter models, at least when one is concerned with translation-invariant measures on the state space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Andjel, Ergodic and mixing properties of equivalence measures for Markov processes,Trans. Am. Math. Soc. 318:601–614 (1990).
R. Durrett,Probability: Theory and Examples (Wadsworth, Pacific Grove, California, 1990).
R. Durrett,Lecture Notes on Particle Systems and Percolation (Wadsworth, Pacific Grove, California, 1988).
E. Grannan and G. Swindle, Rigourous results on path properties of catalytic surfaces,J. Stat. Phys. 61:1085–1103 (1990).
P. Hall and C. Hyde,Martingale Limit Theory and Its Applications (Academic, New York, 1980).
T. M. Liggett,Interacting Particle Systems (Springer, New York, 1985).
R. Phelps,Lectures on Choquets Theorem (Van Nostrand, New York, 1966).
Author information
Authors and Affiliations
Additional information
Research supported by P.M.S. 9157461.
Rights and permissions
About this article
Cite this article
Mountford, T.S. Generalized voter models. J Stat Phys 67, 303–311 (1992). https://doi.org/10.1007/BF01049036
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01049036