Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Almost sure functional central limit theorem for ballistic random walk in random environment

Firas Rassoul-Agha and Timo Seppäläinen

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Abstract

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.

Résumé

Nous considérons une marche aléatoire multidimensionnelle en environnement aléatoire produit. La marche est à pas bornés, transiente dans une direction spatiale donnée, et telle que le temps de régénération posséde un moment suffisamment haut. Nous prouvons un principe d’invariance, ou un théorème limite central fonctionnel, sous presque tout environnement pour la marche centrée et diffusivement normalisée. Le point principal derrière le principe d’invariance est que la moyenne trempée (quenched) de la marche est sous-diffusive.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 2 (2009), 373-420.

Dates
First available in Project Euclid: 29 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1241024674

Digital Object Identifier
doi:10.1214/08-AIHP167

Mathematical Reviews number (MathSciNet)
MR2521407

Zentralblatt MATH identifier
1176.60087

Subjects
Primary: 60K37: Processes in random environments 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Random walk Ballistic Random environment Central limit theorem Invariance principle Point of view of the particle Environment process Green function

Citation

Rassoul-Agha, Firas; Seppäläinen, Timo. Almost sure functional central limit theorem for ballistic random walk in random environment. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 2, 373--420. doi:10.1214/08-AIHP167. https://projecteuclid.org/euclid.aihp/1241024674


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