Voter model in a random environment in Zd  

作　　者：Zhichao SHAN Dayue CHEN 

机构地区：[1]School of Mathematical Sciences, Peking University, Beijing 100871, China [2]Center for Statistical Science, Peking University, Beijing 100871, China

出　　处：《Frontiers of Mathematics in China》2012年第5期895-905,共11页中国高等学校学术文摘·数学（英文）

摘　　要：We consider the voter model with flip rates determined by {ue, e ∈ Ed}, where Ed is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice Zd. Suppose that {ue, e ∈ Ed} are independent and identically distributed （i.i.d.） random variables satisfying ue ≥ 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.We consider the voter model with flip rates determined by {ue, e ∈ Ed}, where Ed is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice Zd. Suppose that {ue, e ∈ Ed} are independent and identically distributed （i.i.d.） random variables satisfying ue ≥ 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.

关 键 词：Voter model random walk random environment DUALITY 

分 类 号：O211.62[理学—概率论与数理统计] O211.5[理学—数学]