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Article Dans Une Revue Markov Processes And Related Fields Année : 2020

Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature

Résumé

Kinetically constrained models (KCMs) were introduced by physicists to model the liquid-glass transition. They are interacting particle systems on Z^d in which each element of Z^d can be in state 0 or 1 and tries to update its state to 0 at rate q and to 1 at rate 1 − q, provided that a constraint is satisfied. In this article, we prove the first non-perturbative result of convergence to equilibrium for KCMs with general constraints: for any KCM in the class termed "supercritical" in dimension 1 and 2, when the initial configuration has product Bernoulli(1 − q') law with q' different from q, the dynamics converges to equilibrium with exponential speed when q is close enough to 1, which corresponds to the high temperature regime.
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Dates et versions

hal-02183930 , version 1 (15-07-2019)

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Citer

Laure Marêché. Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature. Markov Processes And Related Fields, 2020, 26 (5), pp.861-884. ⟨hal-02183930⟩
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