PERCOLATION ON THE STATIONARY DISTRIBUTIONS OF THE VOTER MODEL

• 成果类型: Article
• 署名作者: Rath, Balazs; Valesin, Daniel
• 署名单位: MTA-BME Stochastics Research Group; University of Groningen; Budapest University of Technology & Economics
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1104
• 发表日期: 2017
• 页码: 1899-1951
• 关键词: vacant set; TRANSITION; sharpness; systems

摘要

The voter model on Z(d) 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 (external) stationary distributions is a family of measures a, for a between 0 and 1. A configuration sampled from mu(alpha) is a strongly correlated field of 0's and l's on Zd in which the density of l's is a. 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 l's exhibits a phase transition in a. If the voter model is allowed to have sufficiently spread-out interactions, we prove the same result for d >= 3.