Stationary Distributions for the Voter Model in $d\geq 3$ are Bernoulli Shifts

Allan Sly, Lingfu Zhang

Published 2019-08-26Version 1

For the Voter Model on $\mathbb{Z}^d$, $d\geq 3$, we show that the (extremal) stationary distributions are Bernoulli shifts, and answer an open question asked by Steif and Tykesson. The proof is by explicit constructing the stationary distributions as factors of IID processes on $\mathbb{Z}^d$.