Universality in the bulk of the spectrum for complex sample covariance matrices
Sandrine Péché (2012)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).