Constructing extremal stationary distributions for the Voter Model in $d\geq 3$ as factors of IID

Constructing extremal stationary distributions for the Voter Model in $d\geq 3$ as factors of IID

Probability Seminar

Lingfu Zhang (Princeton)

Thursday, October 24, 2019 -
3:15pm to 4:15pm
Location: 
119 Physics

The Voters Model in $\mathbb{Z}^d$ lattice is a well studied interacting particle system. For $d \geq 3$, 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.

Last updated: 2019/12/14 - 2:31pm