We consider a one-dimensional random walk $(X_n)_{n \times
\mathbb{N}}$ in a random environment of zero or strictly positive drifts. We
establish a full large deviation principle for $X_n/n$ of the correct order
$n/(\log n)^2$ in the low speed regime, valid for almost every environment.
This completes the large deviation picture obtained earlier by Greven and den
Hollander and Gantert and Zeitouni in the case of zero and positive drifts. The
proof uses coarse graining along with concentration of measure techniques.
Publié le : 1999-07-14
Classification:
Random walk in random environment,
large deviations,
coarse graining,
60J15,
60F10,
82C44,
60J80
@article{1022677453,
author = {Pisztora, Agoston and Povel, Tobias},
title = {Large Deviation Principle for Random Walk in a Quenched Random
Environment in the Low Speed Regime},
journal = {Ann. Probab.},
volume = {27},
number = {1},
year = {1999},
pages = { 1389-1413},
language = {en},
url = {http://dml.mathdoc.fr/item/1022677453}
}
Pisztora, Agoston; Povel, Tobias. Large Deviation Principle for Random Walk in a Quenched Random
Environment in the Low Speed Regime. Ann. Probab., Tome 27 (1999) no. 1, pp. 1389-1413. http://gdmltest.u-ga.fr/item/1022677453/