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Journal Article

An invariance principle for biased voter model interfaces

Sun R., Swart Jan M., Yu J.

: Bernoulli vol.27, 1 (2021), p. 615-636

: GA19-07140S, GA ČR

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

: 10.3150/20-BEJ1252



(eng): 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.

: BA

: 10103