Probability Seminar

Feng LiangCornell University
Exact sampling and mixing time of Activated Random Walk

Monday, September 27, 2021 - 3:45pm
Malott 406

Abstract: Activated Random Walk is an interacting particle system on the d-dimensional lattice Z^d. On a finite subset V of Z^d it defines a Markov chain on the set of all configurations V -> {0,1}. We prove that when V is a Euclidean ball intersected with Z^d, the mixing time is at most (1+o(1)) times the volume of the ball. The proof uses an exact sampling algorithm for the stationary distribution, a coupling with internal DLA, and an upper bound on the time when internal DLA fills the entire ball. We conjecture cutoff at time zeta times the volume of the ball, where zeta<1 is the limiting density of the stationary state. Joint work with Lionel Levine.