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

## TL;DR

This paper proves that the d-dimensional East model, a kinetically constrained particle system, converges exponentially fast to equilibrium, extending understanding beyond previous stretched exponential results.

## Contribution

It establishes exponential convergence to equilibrium for the d-dimensional East model, a significant advancement over prior stretched exponential convergence proofs.

## Key findings

- Exponential convergence proven for all settings where convergence is possible.
- Extends understanding of the d-dimensional East model beyond previous results.
- Provides rigorous mathematical proof of convergence rate.

## Abstract

Kinetically constrained models (KCMs) are interacting particle systems on $Z^d$ 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.