Universality in the bulk of the spectrum for complex sample covariance matrices
Péché, Sandrine
Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012), p. 80-106 / Harvested from Numdam
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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 ≤ i ≤ N, 1≤j ≤ p, 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, ∞).

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 ≤ i ≤ N, 1 ≤ j ≤ p, 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, ∞).

Publié le : 2012-01-01
DOI : https://doi.org/10.1214/11-AIHP442
Classification:  60B20,  60B10,  60B12 
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     author = {P\'ech\'e, Sandrine},
     title = {Universality in the bulk of the spectrum for complex sample covariance matrices},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {48},
     year = {2012},
     pages = {80-106},
     doi = {10.1214/11-AIHP442},
     mrnumber = {2919199},
     zbl = {1238.60010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2012__48_1_80_0}
}

Péché, Sandrine. Universality in the bulk of the spectrum for complex sample covariance matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) pp. 80-106. doi : 10.1214/11-AIHP442. http://gdmltest.u-ga.fr/item/AIHPB_2012__48_1_80_0/

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