Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime

Nathanaël Enriquez (1, 2) , Christophe Sabot (3) , Olivier Zindy (1, 4)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 ICJ - Institut Camille Jordan
4 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of ''valleys" of height $\log t$. In the quenched setting, we also sharply estimate the distribution of the walk at time $t$.

Mots clés: Random walk in random environment; aging; quenched localization

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy. Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime. Bulletin de la société mathématique de France, 2009, 137, pp.423-452. ⟨hal-00185933v3⟩