A note on quenched moderate deviations for Sinai's random walk in random environment
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 56-65.

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

DOI : 10.1051/ps:2004001
Classification : 60F10, 60K37
Mots clés : random walk in random environment, Sinai’s regime, $t$-stable point, moderate deviations
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     title = {A note on quenched moderate deviations for {Sinai's} random walk in random environment},
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     url = {http://archive.numdam.org/articles/10.1051/ps:2004001/}
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Comets, Francis; Popov, Serguei. A note on quenched moderate deviations for Sinai's random walk in random environment. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 56-65. doi : 10.1051/ps:2004001. http://archive.numdam.org/articles/10.1051/ps:2004001/

[1] F. Comets and S.Yu. Popov, Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment. Probab. Theory Relat. Fields 126 (2003) 571-609. | Zbl

[2] A. Greven and F. Den Hollander, Large deviations for a random walk in random environment. Ann. Probab. 22 (1994) 1381-1428. | MR | Zbl

[3] Y. Hu and Z. Shi, The limits of Sinai's simple random walk in random environment. Ann. Probab. 26 (1998) 1477-1521. | Zbl

[4] Y. Hu and Z. Shi, Moderate deviations for diffusions with Brownian potentials. (2003) Preprint PMA-792 available at http://www.proba.jussieu.fr/mathdoc/preprints/index.html#2003 | Zbl

[5] B. Hughes, Random Walks and Random Environments. Vol. 2. Random Environments. The Clarendon Press, Oxford University Press, New York (1996). | MR | Zbl

[6] Z. Shi, Sinai's Walk via Stochastic Calculus, in Milieux Aléatoires, F. Comets and E. Pardoux Eds., Société Mathématique de France, Paris, Panoramas et Synthèses 12 (2001). | Zbl

[7] A. Shiryaev, Probability. 2nd edn., Springer, New York (1989). | MR | Zbl

[8] Ya.G. Sinai, The limiting behavior of one-dimensional random walk in random medium. Theory Probab. Appl. 27 (1982) 256-268. | MR | Zbl

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

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