We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Publié le : 2009-05-15
Classification:
Random walk,
Ballistic,
Random environment,
Central limit theorem,
Invariance principle,
Point of view of the particle,
Environment process,
Green function,
60K37,
60F05,
60F17,
82D30
@article{1241024674,
author = {Rassoul-Agha, Firas and Sepp\"al\"ainen, Timo},
title = {Almost sure functional central limit theorem for ballistic random walk in random environment},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 373-420},
language = {en},
url = {http://dml.mathdoc.fr/item/1241024674}
}
Rassoul-Agha, Firas; Seppäläinen, Timo. Almost sure functional central limit theorem for ballistic random walk in random environment. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 373-420. http://gdmltest.u-ga.fr/item/1241024674/