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

2011/04/26 by Ke Wang, Wang, Ke · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1104.4832

openalex publication_date 2011/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the universality of the eigenvalue statistics of the covariance matrices (1)/(n)M^* M where M is a large p× n matrix obeying condition \bfC1. 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 \citetvcovariance from the bulk of the spectrum up to the edge.

Citations

• Random matrices: Universality of local eigenvalue statistics
• On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

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• Tracy-Widom law for the extreme eigenvalues of sample correlation matrices

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