EQUILIBRIUM INTERFACES OF BIASED VOTER MODELS

• 成果类型: Article
• 署名作者: Sun, Rongfeng; Swart, Jan M.; Yu, Jinjiong
• 署名单位: National University of Singapore; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; New York University; NYU Shanghai
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1461
• 发表日期: 2019
• 页码: 2556-2593
• 关键词: tightness; CONVERGENCE

摘要

A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is positive recurrent. In a biological setting, this describes two populations that do not mix, and it is believed to be a common phenomenon in one-dimensional particle systems. Interface tightness has been proved for voter models satisfying a finite second moment condition on the rates. We extend this to biased voter models. Furthermore, we show that the distribution of the equilibrium interface for the biased voter model converges to that of the voter model when the bias parameter tends to zero. A key ingredient is an identity for the expected number of boundaries in the equilibrium voter model interface, which is of independent interest.