We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2+ɛ moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Publié le : 2007-01-14
Classification:
Random walk in random environment,
point of view of particle,
renewal,
invariant measure,
invariance principle,
functional central limit theorem,
60K37,
60F17,
82D30
@article{1174324122,
author = {Rassoul-Agha, Firas and Sepp\"al\"ainen, Timo},
title = {Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1-31},
language = {en},
url = {http://dml.mathdoc.fr/item/1174324122}
}
Rassoul-Agha, Firas; Seppäläinen, Timo. Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction. Ann. Probab., Tome 35 (2007) no. 1, pp. 1-31. http://gdmltest.u-ga.fr/item/1174324122/