0534730 20240103224747.820201120235959.9 85097471750 000592642200025 10.3150/20-BEJ1252 22 s. P cav_un_epca*02522181350-7265271 (2021)615-636International Statistical Institute biased voter model branching and coalescing random walks interface tightness invariance principle cav_un_auth*0253274 Sun R. SG cav_un_auth*0217893 Swart Jan M. UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ 33 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0266677 Yu J. CN 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 GA19-07140S GA ČR CZ cav_un_auth*0385132 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. WOS BA 10000 10100 10103 2022 3 4 A sml 4as 20231122145311.3 RVO:67985556 http://hdl.handle.net/11104/0313195 cav_un_auth*0319768 National University of Singapore NUS SG cav_un_auth*0377457 New York University, Shanghai CN S Copyright transfer agreement 20200904 3+4 Article Statistics Probability C STATISTICS&PROBABILITY 1.781 0.519 8.9 0.00924 1.704 3422 80 1.764 35.52 1.85 689 Q1 1.753 106 Q2 58.8 Q1 Q1 0.77 Q2 58.8 2021 Soubory v repozitáři: swart-0534730-copyright-scan.pdf 85097471750 SCOPUS PUBMED 000592642200025 WOS cav_un_epca*0252218 Bernoulli 1350-7265 1573-9759 Roč. 27 č. 1 2021 615 636 International Statistical Institute