2019/08/08 by Rongfeng Sun, Sun, Rongfeng, Jan M. Swart +3
Mathematics · Physics and Astronomy · #60K35 #82C22 #82C24 #82C41 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Opinion Dynamics and Social Influence #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1908.02944
openalex publication_date 2019/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.