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doi:10.1007/s11464-012-0228-z

Front Math Chin

2012, Vol. 7

Issue (5) : 895-905 https://doi.org/10.1007/s11464-012-0228-z

RESEARCH ARTICLE

Voter model in a random environment in ?d

Zhichao SHAN¹, Dayue CHEN^1,2(

)

1. School of Mathematical Sciences, Peking University, Beijing 100871, China; 2. Center for Statistical Science, Peking University, Beijing 100871, China

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Abstract

We consider the voter model with flip rates determined by {μ_e, e ∈ E_d}, where E_d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ?d. Suppose that {μ_e, e ∈ E_d} are independent and identically distributed (i.i.d.) random variables satisfying μ_e≥1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: δ₀ and δ₁.

Keywords Voter model random walk random environment duality

Corresponding Author(s): CHEN Dayue,Email:dayue@pku.edu.cn

Issue Date: 01 October 2012

Cite this article:

Zhichao SHAN,Dayue CHEN. Voter model in a random environment in ?d[J]. Front Math Chin, 2012, 7(5): 895-905.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0228-z
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I5/895

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