For the VoterModel 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Bernoulli shift
- Factor of iid.
- Random cluster model
- Voter model