Title :

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

Author(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]

Journal title :

ESAIM: Proceedings and Surveys

Pages :

150-174

Publisher :

EDP Sciences

Publication date :

2015-10

ISSN :

2267-3059

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Traitement Statistique du Signal en grandes dimensions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL