STATIONARY DISTRIBUTIONS FOR THE VOTER MODEL IN d ≥ 3 ARE FACTORS OF IID

Allan Sly; Lingfu Zhang

doi:10.1214/22-AOP1568

STATIONARY DISTRIBUTIONS FOR THE VOTER MODEL IN d ≥ 3 ARE FACTORS OF IID

Allan Sly, Lingfu Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For the VoterModel on Z^d, d ≥ 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899–955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Z^d.

Original language	English (US)
Pages (from-to)	1589-1609
Number of pages	21
Journal	Annals of Probability
Volume	50
Issue number	4
DOIs	https://doi.org/10.1214/22-AOP1568
State	Published - Jul 2022

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bernoulli shift
Factor of iid.
Random cluster model
Voter model

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10.1214/22-AOP1568

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abstract = "For the VoterModel on Zd, d ≥ 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899–955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Zd.",

keywords = "Bernoulli shift, Factor of iid., Random cluster model, Voter model",

author = "Allan Sly and Lingfu Zhang",

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doi = "10.1214/22-AOP1568",

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AU - Sly, Allan

AU - Zhang, Lingfu

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2022

PY - 2022/7

Y1 - 2022/7

N2 - For the VoterModel on Zd, d ≥ 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899–955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Zd.

AB - For the VoterModel on Zd, d ≥ 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899–955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Zd.

KW - Bernoulli shift

KW - Factor of iid.

KW - Random cluster model

KW - Voter model

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JO - Annals of Probability

JF - Annals of Probability

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ER -

STATIONARY DISTRIBUTIONS FOR THE VOTER MODEL IN d ≥ 3 ARE FACTORS OF IID

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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