Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Process-level quenched large deviations for random walk in random environment

Firas Rassoul-Agha and Timo Seppäläinen

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Abstract

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.

Résumé

Nous considérons une marche aléatoire en environment aléatoire ergodique. La marche est elliptique et à pas bornés. Nous prouvons un principe de grandes déviations au niveau 3, sous presque tout environnement, avec une fonctionnelle d’action liée à une entropie relative.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 1 (2011), 214-242.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1294170236

Digital Object Identifier
doi:10.1214/10-AIHP369

Mathematical Reviews number (MathSciNet)
MR2779403

Zentralblatt MATH identifier
1298.60097

Subjects
Primary: 60K37: Processes in random environments 60F10: Large deviations 82D30: Random media, disordered materials (including liquid crystals and spin glasses) 82C44: Dynamics of disordered systems (random Ising systems, etc.)

Keywords
Random walk Random environment RWRE Large deviation Environment process Relative entropy Homogenization

Citation

Rassoul-Agha, Firas; Seppäläinen, Timo. Process-level quenched large deviations for random walk in random environment. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 1, 214--242. doi:10.1214/10-AIHP369. https://projecteuclid.org/euclid.aihp/1294170236


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