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

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

2011-04-26

arxiv.org/abs/1104.4832v1

Mathematics

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20 pages, 2 figures

Scientific paper

We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where $M$ is a large $p\times n$ matrix obeying condition $\bf{C1}$. 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.

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