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

Nathanaël Enriquez; Christophe Sabot; Olivier Zindy

Bulletin de la Société Mathématique de France (2009)

  • Volume: 137, Issue: 3, page 423-452
  • ISSN: 0037-9484

Abstract

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We consider transient one-dimensional random walks in a 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 .

How to cite

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Enriquez, Nathanaël, Sabot, Christophe, and Zindy, Olivier. "Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime." Bulletin de la Société Mathématique de France 137.3 (2009): 423-452. <http://eudml.org/doc/272482>.

@article{Enriquez2009,
abstract = {We consider transient one-dimensional random walks in a 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 $t$.},
author = {Enriquez, Nathanaël, Sabot, Christophe, Zindy, Olivier},
journal = {Bulletin de la Société Mathématique de France},
keywords = {random walks in random environment; aging; quenched localisation},
language = {eng},
number = {3},
pages = {423-452},
publisher = {Société mathématique de France},
title = {Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime},
url = {http://eudml.org/doc/272482},
volume = {137},
year = {2009},
}

TY - JOUR
AU - Enriquez, Nathanaël
AU - Sabot, Christophe
AU - Zindy, Olivier
TI - Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
JO - Bulletin de la Société Mathématique de France
PY - 2009
PB - Société mathématique de France
VL - 137
IS - 3
SP - 423
EP - 452
AB - We consider transient one-dimensional random walks in a 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 $t$.
LA - eng
KW - random walks in random environment; aging; quenched localisation
UR - http://eudml.org/doc/272482
ER -

References

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