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arXiv · 1905.00765

Exponential convergence to equilibrium for the d-dimensional East model

Laure Marêché
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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.

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Laure Marêché. 2019-09-20. Exponential convergence to equilibrium for the d-dimensional East model. https://doi.org/10.1214/19-ecp261

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