Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
- Enriquez, N.
- Sabot, C.
- Zindy, O.
2010 Mathematics Subject Classification
- 60K37 60G50 60J45 82D30
- Random walk in random environment; aging; quenched, localization
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 $t$.