Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature

Abstract

Kinetically constrained models (KCMs) were introduced by physicists to model the liquid-glass transition. They are interacting particle systems on ${\mathbb{Z}}^d$ in which each element of ${\mathbb{Z}}^d$ can be in state 0 or 1 and tries to update its state to 0 at rate $q$ and to 1 at rate $1-q$, provided that a constraint is satisfied. In this article, we prove the first non-perturbative result of convergence to equilibrium for KCMs with general constraints: for any KCM in the class termed "supercritical" in dimension 1 and 2, when the initial configuration has product $\mathrm{Bernoulli}(1-q^{\prime })$ law with $q^{\prime }\ne q$, the dynamics converges to equilibrium with exponential speed when $q$ is close enough to 1, which corresponds to the high temperature regime.

17 pages, 4 figures

References in corpus (5)

• Universality results for kinetically constrained spin models in two dimensions
• Fredrickson-Andersen one spin facilitated model out of equilibrium
• Exponential convergence to equilibrium for the d-dimensional East model
• Mixing time and local exponential ergodicity of the East-like process in ${\mathbf{Z}}^d$
• Universality for critical KCM: infinite number of stable directions