= Invariant measures of the two-dimensional voter model
{title2=$\alpha\delta_0+(1-\alpha)\delta_1$}
In a nearest-neighbor <voter model> on the <square lattice>, any two ancestral <coalescing random walks> meet almost surely. For an <invariant probability measure of a Markov process>, the disagreement <probability> is constant in time but bounded by the vanishing <probability> of noncoalescence. Hence every pair of sites agrees almost surely. Countability concentrates the measure on the two constant configurations; both are <absorbing state>, so every mixture of their <Dirac measures> is invariant. <Translation invariance> need not be assumed.
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