For the Voter Model on , , 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 .
This work was supported by an NSF career award (DMS-1352013), a Simons Investigator grant and a MacArthur Fellowship.
The authors would like to thank Jeff Steif for suggesting the problem. We are also very thankful for the many helpful suggestions from an anonymous referee, who pointed out an error in the first version of this paper, and suggested a simplification in the construction of and in Section 2.2.
"Stationary distributions for the voter model in are factors of IID." Ann. Probab. 50 (4) 1589 - 1609, July 2022. https://doi.org/10.1214/22-AOP1568