# Stable fluctuations for ballistic random walks in random environment on Z

Abstract : We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitting time of level $n$, after proper centering and normalization, converges to a completely asymmetric stable distribution, but does not describe its scale parameter. Following a previous article by three of the authors, where the (non-critical) zero speed case was dealt with, we give a new proof of this result in the subdiffusive case that provides a complete description of the limit law. The case of Dirichlet environment turns out to be remarkably explicit.
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2010
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-00467052
Contributor : Laurent Tournier <>
Submitted on : Thursday, March 25, 2010 - 6:17:54 PM
Last modification on : Saturday, November 11, 2017 - 1:12:30 AM
Document(s) archivé(s) le : Monday, June 28, 2010 - 4:44:45 PM

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### Identifiers

• HAL Id : hal-00467052, version 1
• ARXIV : 1004.1333

### Citation

Nathanaël Enriquez, Christophe Sabot, Laurent Tournier, Olivier Zindy. Stable fluctuations for ballistic random walks in random environment on Z. 2010. 〈hal-00467052〉

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