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