Translator Disclaimer
February 2012 Universality in the bulk of the spectrum for complex sample covariance matrices
Sandrine Péché
Ann. Inst. H. Poincaré Probab. Statist. 48(1): 80-106 (February 2012). DOI: 10.1214/11-AIHP442

Abstract

We consider complex sample covariance matrices MN = (1/N)YY* where Y is a N × p random matrix with i.i.d. entries Yij, 1 ≤ iN, 1 ≤ jp, with distribution F. Under some regularity and decay assumptions on F, we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where N → ∞ and limN→∞p/N = γ for any real number γ ∈ (0, ∞).

On considère des matrices de covariance empirique complexes MN = (1/N)YY* où Y est une matrice de taille N × p dont les coefficients Yij, 1 ≤ iN, 1≤jp, sont des variables aléatoires i.i.d. de loi F. Sous certaines hypothèses de régularité et de décroissance sur F, on montre l’universalité de certaines statistiques locales de valeurs propres au milieu du spectre quand N → ∞ et limN→∞p/N = γ pour tout réel γ ∈ (0, ∞).

Citation

Download Citation

Sandrine Péché. "Universality in the bulk of the spectrum for complex sample covariance matrices." Ann. Inst. H. Poincaré Probab. Statist. 48 (1) 80 - 106, February 2012. https://doi.org/10.1214/11-AIHP442

Information

Published: February 2012
First available in Project Euclid: 23 January 2012

zbMATH: 1238.60010
MathSciNet: MR2919199
Digital Object Identifier: 10.1214/11-AIHP442

Subjects:
Primary: 60B10, 60B12, 60B20

Rights: Copyright © 2012 Institut Henri Poincaré

JOURNAL ARTICLE
27 PAGES


SHARE
Vol.48 • No. 1 • February 2012
Back to Top