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The Infinite Atlas Process: Convergence to Equilibrium

Dembo, Amir; Jara, Milton; Olla, Stefano (2018), The Infinite Atlas Process: Convergence to Equilibrium, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

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https://hal.archives-ouvertes.fr/hal-01584723
Date
2018
Nom de la revue
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Métadonnées
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Auteur(s)
Dembo, Amir
Department of Statistics [Stanford]
Jara, Milton
Instituto Nacional de Matemática Pura e Aplicada [IMPA]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
The semi-infinite Atlas process is a one-dimensional system of Brownian particles, where only the leftmost particle gets a unit drift to the right. Its particle spacing process has infinitely many stationary measures, with one distinguished translation invariant reversible measure. We show that the latter is attractive for a large class of initial configurations of slowly growing (or bounded) particle densities. Key to our proof is a new estimate on the rate of convergence to equilibrium for the particle spacing in a triangular array of finite, large size systems.
Mots-clés
infinite Atlas process; Interacting particles; reflecting Brownian motions; non-equilibrium hydrodynamics