On the concentration 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 consider Sinai's random walk in random environment. We prove that for an interval of time [1,n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi totality of this amount of time. Moreover the local time at the point of localization normalized by $n$ converges in probability to a well defined random variable of the environment.

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

Domaines: Probabilités [math.PR]

Pierre Andreoletti. On the concentration of Sinai's walk. 2005. ⟨hal-00002924⟩