Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.27 • No. 1 • February 2021
Back to Top