Strong Central Limit Theorem for isotropic random walks in Rd

TitreStrong Central Limit Theorem for isotropic random walks in Rd
Type de publicationArticle de revue
AuteurGraczyk, Piotr , Loeb, Jean-Jacques , Żak, Tomasz
PaysAllemagne
EditeurSpringer
VilleBerlin ; Heidelberg
TypeArticle scientifique dans une revue à comité de lecture
Année2011
LangueAnglais
Date2011/10/01
Numéro1-2
Pagination153 - 172
Volume151
Titre de la revueProbability Theory and Related Fields
ISSN1432-2064
Mots-clésAnalyse, Probabilités et Statistique, Central, Gaussian, Logarithmic, Mathematical, Operations, Probability, Quantitative, Random, Statistics, Theoretical, Mathematical and Computational Physics
Résumé en anglais

We prove an optimal Gaussian upper bound for the densities of isotropic random walks on Rd in spherical case (d ≥ 2) and ball case (d ≥ 1). We deduce the strongest possible version of the Central Limit Theorem for the isotropic random walks: if S~n denotes the normalized random walk and Y the limiting Gaussian vector, then Ef(S~n)→Ef(Y) for all functions f integrable with respect to the law of Y. We call such result a “Strong CLT”. We apply our results to get strong hypercontractivity inequalities and strong Log-Sobolev inequalities.

URL de la noticehttp://okina.univ-angers.fr/publications/ua127
DOI10.1007/s00440-010-0295-6
Lien vers le document

http://dx.doi.org/10.1007/s00440-010-0295-6