Ráth, Balázs and Valesin, Daniel
(2015)
Percolation on the stationary distributions of the voter model.
Annals of Probability.
ISSN 0091-1798
(In Press)
Abstract
The voter model on Zd is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When d≥3, the set of (extremal) stationary distributions is a family of measures μα, for α between 0 and 1. A configuration sampled from μα is a strongly correlated field of 0's and 1's on Zd in which the density of 1's is α. We consider such a configuration as a site percolation model on Zd. We prove that if d≥5, the probability of existence of an infinite percolation cluster of 1's exhibits a phase transition in α. If the voter model is allowed to have sufficiently spread-out interactions, we prove the same result for d≥3.
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