An invariance principle for biased voter model interfaces

0534730 - ÚTIA 2022 RIV NL eng J - Journal Article
Sun, R. - Swart, Jan M. - Yu, J.
An invariance principle for biased voter model interfaces.
Bernoulli. Roč. 27, č. 1 (2021), s. 615-636. ISSN 1350-7265. E-ISSN 1573-9759
R&D Projects: GA ČR(CZ) GA19-07140S
Institutional support: RVO:67985556
Keywords : biased voter model * branching and coalescing random walks * interface tightness * invariance principle
OECD category: Statistics and probability
Impact factor: 1.822, year: 2021
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2020/SI/swart-0534730.pdf https://projecteuclid.org/journals/annals-of-probability/volume-6/issue-2/Stopping-Times-and-Tightness/10.1214/aop/1176995579.full

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.
Permanent Link: http://hdl.handle.net/11104/0313195