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July 1999 Large Deviation Principle for Random Walk in a Quenched Random Environment in the Low Speed Regime
Agoston Pisztora, Tobias Povel
Ann. Probab. 27(3): 1389-1413 (July 1999). DOI: 10.1214/aop/1022677453

Abstract

We consider a one-dimensional random walk $(X_n)_{n \times \mathbb{N}}$ in a random environment of zero or strictly positive drifts. We establish a full large deviation principle for $X_n/n$ of the correct order $n/(\log n)^2$ in the low speed regime, valid for almost every environment. This completes the large deviation picture obtained earlier by Greven and den Hollander and Gantert and Zeitouni in the case of zero and positive drifts. The proof uses coarse graining along with concentration of measure techniques.

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Agoston Pisztora. Tobias Povel. "Large Deviation Principle for Random Walk in a Quenched Random Environment in the Low Speed Regime." Ann. Probab. 27 (3) 1389 - 1413, July 1999. https://doi.org/10.1214/aop/1022677453

Information

Published: July 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0964.60056
MathSciNet: MR1733154
Digital Object Identifier: 10.1214/aop/1022677453

Subjects:
Primary: 60F10, 60J15, 60J80, 82C44

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 3 • July 1999
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