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A note on quenched moderate deviations for Sinai's random walk in random environment

Published online by Cambridge University Press:  15 September 2004

Francis Comets  and
Serguei Popov
Francis Comets
Affiliation:
Université Paris 7, UFR de Mathématiques, case 7012, 2, place Jussieu, 75251 Paris Cedex 05, France; e-mail: Partially supported by CNRS (UMR 7599 “Probabilités et Modèles Aléatoires”) and by the “Réseau Mathématiques France-Brésil”.
Serguei Popov
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508–090, São Paulo SP, Brasil; e-mail: Partially supported by CNPq (302981/02–0), and by the “Rede Matemática Brasil-França".
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Abstract

We consider the continuous time, one-dimensional random walk in random environmentin Sinai's regime. We show that the probability for theparticle to be, at time t and in a typical environment,at a distance larger than ta (0<a<1)from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.

Keywords

Random walk in random environmentSinai's regimet-stable pointmoderate deviations.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 56 - 65
Copyright
© EDP Sciences, SMAI, 2004

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References

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O. Zeitouni, Lecture Notes on Random Walks in Random Environment. (2003) Preliminary version at www-ee.technion.ac.il/~zeitouni/ps/notes1.ps