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

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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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