Alternative proof for the localization of Sinai's walk

Pierre Andreoletti (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood.

Mots clés: random environment; random walk; Sinai's regime; Markov chain

Domaines: Probabilités [math.PR]

Pierre Andreoletti. Alternative proof for the localization of Sinai's walk. 2005. ⟨hal-00002922⟩