
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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Article accepté pour publication ou publiéExternal document link
https://hal.archives-ouvertes.fr/hal-01584723Date
2018Journal name
Annales de l'Institut Henri Poincaré (B) Probabilités et StatistiquesMetadata
Show full item recordAuthor(s)
Dembo, AmirDepartment of Statistics [Stanford]
Jara, Milton
Instituto Nacional de Matemática Pura e Aplicada [IMPA]
Olla, Stefano

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (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.Subjects / Keywords
infinite Atlas process; Interacting particles; reflecting Brownian motions; non-equilibrium hydrodynamicsRelated items
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