Universality in the bulk of the spectrum for complex sample covariance matrices

2009/12/13 by Péché, S.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0912.2493

Abstract

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

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