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}
}
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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