An invariance principle for biased voter model interfaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
An invariance principle for biased voter model interfaces
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastic Evolution Equations and Space-Time Systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bernoulli
ISSN
1350-7265
e-ISSN
1573-9759
Volume of the periodical
27
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
22
Pages from-to
615-636
UT code for WoS article
000592642200025
EID of the result in the Scopus database
2-s2.0-85097471750