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Exponential convergence to equilibrium for the \(d\)-dimensional East model. (English) Zbl 1422.60160
Summary: 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 P. Chleboun et al. [Ann. Fac. Sci. Toulouse, Math. (6) 24, No. 4, 717–743 (2015; Zbl 1333.60199)]. We show that the \(d\)-dimensional East model exhibits exponential convergence to equilibrium in all settings for which convergence is possible.
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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