Stable fluctuations for ballistic random walks in random environment on Z

2010/04/08 by Enriquez, Nathanaël, Sabot, Christophe, Tournier, Laurent +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1004.1333

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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