Exponential convergence to equilibrium for the $d$-dimensional East model

Abstract

Kinetically constrained models (KCMs) are interacting particle systems on $\mathbb{Z} ^{d}$ with a continuous-time constrained Glauber dynamics, which were introduced by physicists to model the liquid-glass transition. One of the most well-known KCMs is the one-dimensional East model. Its generalization to higher dimension, the $d$-dimensional East model, is much less understood. Prior to this paper, convergence to equilibrium in the $d$-dimensional East model was proven to be at least stretched exponential, by Chleboun, Faggionato and Martinelli in 2015. We show that the $d$-dimensional East model exhibits exponential convergence to equilibrium in all settings for which convergence is possible.