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.
Mots-clés : random walk, ballistic, random environment, central limit theorem, invariance principle, point of view of the particle, environment process, Green function
@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},
pages = {373--420},
publisher = {Gauthier-Villars},
volume = {45},
number = {2},
year = {2009},
doi = {10.1214/08-AIHP167},
mrnumber = {2521407},
zbl = {1176.60087},
language = {en},
url = {http://www.numdam.org/articles/10.1214/08-AIHP167/}
}
TY - JOUR AU - Rassoul-Agha, Firas AU - Seppäläinen, Timo TI - Almost sure functional central limit theorem for ballistic random walk in random environment JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 373 EP - 420 VL - 45 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP167/ DO - 10.1214/08-AIHP167 LA - en ID - AIHPB_2009__45_2_373_0 ER -
%0 Journal Article %A Rassoul-Agha, Firas %A Seppäläinen, Timo %T Almost sure functional central limit theorem for ballistic random walk in random environment %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 373-420 %V 45 %N 2 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/08-AIHP167/ %R 10.1214/08-AIHP167 %G en %F 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) no. 2, pp. 373-420. doi : 10.1214/08-AIHP167. http://www.numdam.org/articles/10.1214/08-AIHP167/
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