Electronic Communications in Probability

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

Laure Marêché

Full-text: Open access

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.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 55, 10 pp.

Dates
Received: 2 May 2019
Accepted: 19 August 2019
First available in Project Euclid: 13 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1568361881

Digital Object Identifier
doi:10.1214/19-ECP261

Mathematical Reviews number (MathSciNet)
MR4003129

Zentralblatt MATH identifier
1422.60160

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
interacting particle systems Glauber dynamics kinetically constrained models East model convergence to equilibrium

Rights
Creative Commons Attribution 4.0 International License.

Citation

Marêché, Laure. Exponential convergence to equilibrium for the $d$-dimensional East model. Electron. Commun. Probab. 24 (2019), paper no. 55, 10 pp. doi:10.1214/19-ECP261. https://projecteuclid.org/euclid.ecp/1568361881


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References

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