Voter-model duality
= Voter-model duality
{title2=$\xi_t(x)=\xi_0(X_t^x)$}
Independent <Poisson process> copying arrows construct the <voter model>. A backward ancestral line from a site follows a <continuous-time random walk>; lines that meet then coincide. Thus a finite collection of <Ising spins> at time $t$ equals initial <Ising spins> at the positions of <coalescing random walks>. In particular $E_\eta\xi_t(x)=\sum_zp_t(x,z)\eta(z)$, and the <probability> of disagreement at two sites is bounded by the <probability> their ancestral walks have not yet coalesced.