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August 2019 Equilibrium interfaces of biased voter models
Rongfeng Sun, Jan M. Swart, Jinjiong Yu
Ann. Appl. Probab. 29(4): 2556-2593 (August 2019). DOI: 10.1214/19-AAP1461

Abstract

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.

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Rongfeng Sun. Jan M. Swart. Jinjiong Yu. "Equilibrium interfaces of biased voter models." Ann. Appl. Probab. 29 (4) 2556 - 2593, August 2019. https://doi.org/10.1214/19-AAP1461

Information

Received: 1 April 2018; Revised: 1 October 2018; Published: August 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07120716
MathSciNet: MR3984257
Digital Object Identifier: 10.1214/19-AAP1461

Subjects:
Primary: 60K35 , 82C22
Secondary: 60K35 , 82C24 , 82C41

Keywords: Biased voter model , branching and coalescing random walks , interface tightness

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 4 • August 2019
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