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Mixing time and local exponential ergodicity of the East-like process in d
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Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 717-743.

The East process, a well known reversible linear chain of spins, represents the prototype of a general class of interacting particle systems with constraints modeling the dynamics of real glasses. In this paper we consider a generalization of the East process living in the d-dimensional lattice and we establish new progresses on the out-of-equilibrium behavior. Despite the fact that convergence to the stationary reversible measure in the uniform norm cannot hold because of the presence of blocked configurations, we prove a form of (local) exponential ergodicity when the initial distribution is different from the stationary one. We also establish that the mixing time in a finite box grows linearly in the side of the box.

Le processus East est une chaîne linéaire de spins réversible et bien connue, qui représente le prototype d’une classe générale de systèmes de particules en interaction avec des contraintes modélisant des dynamiques vitreuses réelles. Dans ce papier, nous considérons une généralisation d-dimensionnelle du processus East et nous obtenons de nouveaux comportements hors équilibre. Bien que la convergence à l’équilibre réversible ne puisse pas avoir lieu en norme uniforme, de par la présence de configurations bloquantes, nous prouvons une ergodicité exponentielle locale pour les distributions initiales différentes de la probabilité stationnaire. Nous établissons également la croissance linéaire en la taille de la boîte du temps de mélange dans une boîte finie.

Published online : 2016-01-21
@article{AFST_2015_6_24_4_717_0,
     author = {Paul Chleboun and Alessandra Faggionato and Fabio Martinelli},
     title = {Mixing time and local exponential ergodicity of the East-like process in $\mathbb{Z}^d$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {4},
     year = {2015},
     pages = {717-743},
     language = {en},
     url={afst.centre-mersenne.org/item/AFST_2015_6_24_4_717_0/}
}
Chleboun, Paul; Faggionato, Alessandra; Martinelli, Fabio. Mixing time and local exponential ergodicity of the East-like process in $\mathbb{Z}^d$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 717-743. https://afst.centre-mersenne.org/item/AFST_2015_6_24_4_717_0/

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