Stationary distributions for the voter model in d≥3 are factors of IID

Abstract

For the Voter Model on Zd, d≥3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899–955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Zd.