Random covariance matrices: Universality of local statistics of eigenvalues up to the edge

Abstract

We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}{M}^{\ast }M$ where $M$ is a large $p\times n$ matrix obeying condition $C1$. In particular, as an application, we prove a variant of universality results regarding the smallest singular value of $M_{p,n}$. This paper is an extension of the results in \cite{tvcovariance} from the bulk of the spectrum up to the edge.

20 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:0912.0966 by other authors

References in corpus (2)

• Local semicircle law and complete delocalization for Wigner random matrices
• Random matrices: Universality of local eigenvalue statistics up to the edge

Cited by in corpus (3)

• Random matrices: The Four Moment Theorem for Wigner ensembles
• Eigenvalue variance bounds for Wigner and covariance random matrices
• Tracy-Widom law for the extreme eigenvalues of sample correlation matrices