# Quenched limits for the fluctuations of transient random walks in random environment on Z

```@article{Enriquez2010QuenchedLF,
title={Quenched limits for the fluctuations of transient random walks in random environment on Z},
author={Nathanael Enriquez and Christophe Sabot and Laurent Tournier and Olivier Zindy},
journal={arXiv: Probability},
year={2010}
}```
• Published 9 December 2010
• Mathematics
• arXiv: Probability
We consider transient nearest-neighbor random walks in random environment on Z. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level n, around its mean, in terms of an explicit function of the environment. Moreover, their limiting law is described using a Poisson point process whose intensity is computed. This result can be considered as the quenched analog of the classical result of Kesten, Kozlov…

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J. Peterson was partially supported by National Science Foundation grant DMS-0802942. G. Samorodnitsky was partially supported by ARO grant W911NF-10-1-0289 and NSF grant DMS-1005903 at Cornell