Constructing extremal stationary distributions for the Voter Model in $d\geq 3$ as factors of IIDConstructing extremal stationary distributions for the Voter Model in d¿3 as factors of IID
The Voters Model in Zd lattice is a well studied interacting particle system. For d¿3, it has a one parameter family of extremal stationary distributions. Steif and Tykesson asked if these stationary distributions are factors of IID, or equivalently, isomorphic to Bernoulli shifts. We give an affirmative answer to this question. Our result also gives the first natural example of the so-called divide and color models, such that each cluster of the partition is infinite, while the coloring process is a factor of IID. It is a joint work with Allan Sly.