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February 2021 An invariance principle for biased voter model interfaces
Rongfeng Sun, Jan M. Swart, Jinjiong Yu
Bernoulli 27(1): 615-636 (February 2021). DOI: 10.3150/20-BEJ1252


We consider one-dimensional biased voter models, where 1’s replace 0’s at a faster rate than the other way round, started in a Heaviside initial state describing the interface between two infinite populations of 0’s and 1’s. In the limit of weak bias, for a diffusively rescaled process, we consider a measure-valued process describing the local fraction of type 1 sites as a function of time. Under a finite second moment condition on the rates, we show that in the diffusive scaling limit there is a drifted Brownian path with the property that all but a vanishingly small fraction of the sites on the left (resp. right) of this path are of type 0 (resp. 1). This extends known results for unbiased voter models. Our proofs depend crucially on recent results about interface tightness for biased voter models.


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Rongfeng Sun. Jan M. Swart. Jinjiong Yu. "An invariance principle for biased voter model interfaces." Bernoulli 27 (1) 615 - 636, February 2021.


Received: 1 March 2020; Revised: 1 July 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282864
MathSciNet: MR4177383
Digital Object Identifier: 10.3150/20-BEJ1252

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

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability


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Vol.27 • No. 1 • February 2021
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