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 (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]

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy. Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime. 2007. ⟨hal-00185933v1⟩