1. School of Mathematical Sciences, Peking University, Beijing 100871, China; 2. Center for Statistical Science, Peking University, Beijing 100871, China
We consider the voter model with flip rates determined by {μe, e ∈ Ed}, where Ed is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ?d. Suppose that {μe, e ∈ Ed} are independent and identically distributed (i.i.d.) random variables satisfying μe≥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.
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