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.
Publié le : 2010-02-15
Classification:
Random walk in random environment,
Law of large numbers,
Large deviations,
Galton–Watson tree,
60K37,
60J80,
60F15,
60F10
@article{1267454113,
author = {Aid\'ekon, Elie},
title = {Large deviations for transient random walks in random environment on a Galton--Watson tree},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 159-189},
language = {en},
url = {http://dml.mathdoc.fr/item/1267454113}
}
Aidékon, Elie. Large deviations for transient random walks in random environment on a Galton–Watson tree. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 159-189. http://gdmltest.u-ga.fr/item/1267454113/