Titre :

A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices

Auteur(s) :

Hachem, Walid [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Hardy, Adrien [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Najim, Jamal [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]

Titre de la revue :

ESAIM: Proceedings and Surveys

Pagination :

150-174

Éditeur :

EDP Sciences

Date de publication :

2015-10

ISSN :

2267-3059

Mot(s)-clé(s) en anglais :

Large random matrices
Wishart matrices
local fluctuations
Airy kernel
Bessel kernel
Pearcey kernel

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Statistiques [math.ST]

Résumé en anglais : [en]

The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart ...
Lire la suite >The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges and cusp points of the spectrum: Under quite general conditions, the eigenvalues fluctuations at a soft edge of the limiting spectrum, at the hard edge when it is present, or at a cusp point, are respectively described by mean of the Airy kernel, the Bessel kernel, or the Pearcey kernel. Moreover, the eigenvalues fluctuations at several soft edges are asymptotically independent. In particular, the asymptotic fluctuations of the matrix condition number can be described. Finally, the next order term of the hard edge asymptotics is provided.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Traitement Statistique du Signal en grandes dimensions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL