Title :

Large complex correlated Wishart matrices: the Pearcey kernel and expansion at the hard edge

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 :

Electronic Journal of Probability
https://projecteuclid.org/journals/electronic-journal-of-probability/volume-21/issue-none/Large-complex-correlated-Wishart-matrices--the-Pearcey-kernel-and/10.1214/15-EJP4441.full

Pages :

1-36

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2016

ISSN :

1083-6489

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as ...
Show more >We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More precisely, under mild assumptions for the population covariance matrix, we show that the limiting density vanishes at generic cusp points like a cube root, and that the local eigenvalue behaviour is described by means of the Pearcey kernel if an extra decay assumption is satisfied. As for the hard edge, we show that the density blows up like an inverse square root at the origin. Moreover, we provide an explicit formula for the 1/N correction term for the fluctuation of the smallest random eigenvalue.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL