Nous considérons une marche aléatoire multidimensionnelle en environnement aléatoire produit. La marche est à pas bornés, transiente dans une direction spatiale donnée, et telle que le temps de régénération posséde un moment suffisamment haut. Nous prouvons un principe d'invariance, ou un théorème limite central fonctionnel, sous presque tout environnement pour la marche centrée et diffusivement normalisée. Le point principal derrière le principe d'invariance est que la moyenne trempée (quenched) de la marche est sous-diffusive.
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.
@article{AIHPB_2009__45_2_373_0,
author = {Rassoul-Agha, Firas and Sepp\"al\"ainen, Timo},
title = {Almost sure functional central limit theorem for ballistic random walk in random environment},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {45},
year = {2009},
pages = {373-420},
doi = {10.1214/08-AIHP167},
mrnumber = {2521407},
zbl = {1176.60087},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2009__45_2_373_0}
}
Rassoul-Agha, Firas; Seppäläinen, Timo. Almost sure functional central limit theorem for ballistic random walk in random environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) pp. 373-420. doi : 10.1214/08-AIHP167. http://gdmltest.u-ga.fr/item/AIHPB_2009__45_2_373_0/
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