Percolation on the stationary distributions of the voter model

Ráth, Balázs and Valesin, Daniel (2017) Percolation on the stationary distributions of the voter model. Annals of Probability, 45 (3). pp. 1899-1951. ISSN 0091-1798

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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.

Item Type:	Article
Subjects:	Q Science / természettudomány > QA Mathematics / matematika
Depositing User:	Dr. Balázs Ráth
Date Deposited:	27 Sep 2017 12:15
Last Modified:	27 Sep 2017 12:15
URI:	http://real.mtak.hu/id/eprint/63992

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• Percolation on the stationary distributions of the voter model. (deposited 23 Sep 2015 03:39)
  • Percolation on the stationary distributions of the voter model. (deposited 01 Oct 2016 05:50)
    • Percolation on the stationary distributions of the voter model. (deposited 27 Sep 2017 12:15) [Currently Displayed]

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