Mixing time and local exponential ergodicity of the East-like process in ${\mathbf{Z}}^d$

Abstract

The East process, a well known reversible linear chain of spins, represents the prototype of a general class of interacting particle systems with constraints modeling the dynamics of real glasses. In this paper we consider a generalization of the East process living in the d-dimensional lattice and we establish new progresses on the out- of-equilibrium behavior. In particular we prove a form of (local) exponential ergodicity when the initial distribution is far from the stationary one and we prove that the mixing time in a finite box grows linearly in the side of the box.

References in corpus (2)

• Calorimetric glass transition explained by hierarchical dynamic facilitation
• Glassy dynamics in the East model

Cited by in corpus (2)

• Exponential convergence to equilibrium for the d-dimensional East model
• Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature