Large deviations for transient random walks in random environment on a Galton–Watson tree

Elie Aidékon

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 1, page 159-189
  • ISSN: 0246-0203

Abstract

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Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.

How to cite

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Aidékon, Elie. "Large deviations for transient random walks in random environment on a Galton–Watson tree." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 159-189. <http://eudml.org/doc/240964>.

@article{Aidékon2010,
abstract = {Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.},
author = {Aidékon, Elie},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walk in random environment; law of large numbers; large deviations; Galton–Watson tree; Galton-Watson tree},
language = {eng},
number = {1},
pages = {159-189},
publisher = {Gauthier-Villars},
title = {Large deviations for transient random walks in random environment on a Galton–Watson tree},
url = {http://eudml.org/doc/240964},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Aidékon, Elie
TI - Large deviations for transient random walks in random environment on a Galton–Watson tree
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 159
EP - 189
AB - Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.
LA - eng
KW - random walk in random environment; law of large numbers; large deviations; Galton–Watson tree; Galton-Watson tree
UR - http://eudml.org/doc/240964
ER -

References

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