An invariance principle for biased voter model interfaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F21%3A00534730" target="_blank" >RIV/67985556:_____/21:00534730 - isvavai.cz</a>

Výsledek na webu

<a href="https://projecteuclid.org/journals/annals-of-probability/volume-6/issue-2/Stopping-Times-and-Tightness/10.1214/aop/1176995579.full" target="_blank" >https://projecteuclid.org/journals/annals-of-probability/volume-6/issue-2/Stopping-Times-and-Tightness/10.1214/aop/1176995579.full</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3150/20-BEJ1252" target="_blank" >10.3150/20-BEJ1252</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An invariance principle for biased voter model interfaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

An invariance principle for biased voter model interfaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastické evoluční rovnice a časoprostorové systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Bernoulli

ISSN

1350-7265

e-ISSN

1573-9759

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

615-636

Kód UT WoS článku

000592642200025

EID výsledku v databázi Scopus

2-s2.0-85097471750