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Licensed Unlicensed Requires Authentication Published by De Gruyter March 25, 2015

Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices

  • Junshan Xie EMAIL logo
From the journal Mathematica Slovaca

Abstract

We consider the number of eigenvalues which fall into an interval for the complex sample covariance matrices. The central limit theorem and a moderate deviation principle are established when the endpoint of the interval is close to the edge of the spectrum. The proofs depend on the Four Moment Theorem about the local statistics of eigenvalues up to edge, and the rigidity theorem of the eigenvalues for sample covariance matrices.

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Received: 2011-12-3
Accepted: 2012-9-25
Published Online: 2015-3-25
Published in Print: 2015-2-1

© 2015 Mathematical Institute Slovak Academy of Sciences

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