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

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

2007-11-07

arxiv.org/abs/0711.1095v3

Mathematics

Probability

24 pages, accepted for publication in "Bulletin de la SMF"

Scientific paper

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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