Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature - Archive ouverte HAL Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
convergence.pdf (537.08 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

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⟩
43 Consultations
22 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More