Random Covariance Matrices: Universality of Local Statistics of Eigenvalues Up to the Edge

K. E. Wang

doi:10.1142/S2010326311500055

Random Covariance Matrices: Universality of Local Statistics of Eigenvalues Up to the Edge

K. E. Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

22 Citations (Scopus)

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 with independent entries that have mean zero, variance one and sufficiently high finite moments. 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 of Tao and Vu (2009) from the bulk of the spectrum up to the edge.

Original language	English
Article number	1150005
Journal	Random Matrices: Theory and Application
Volume	1
Issue number	1
DOIs	https://doi.org/10.1142/S2010326311500055
Publication status	Published - 1 Jan 2012
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2012 World Scientific Publishing Company.

Keywords

Four Moment theorem
Random covariance matrices
universality

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AB - We study the universality of the eigenvalue statistics of the covariance matrices 1/n M M where M is a large p × n matrix with independent entries that have mean zero, variance one and sufficiently high finite moments. In particular, as an application, we prove a variant of universality results regarding the smallest singular value of Mp, n. This paper is an extension of the results of Tao and Vu (2009) from the bulk of the spectrum up to the edge.

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KW - Random covariance matrices

KW - universality

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Random Covariance Matrices: Universality of Local Statistics of Eigenvalues Up to the Edge

Abstract

Bibliographical note

Keywords

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