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2015 Limit theorems for linear eigenvalue statistics of overlapping matrices
Vladislav Kargin
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Electron. J. Probab. 20: 1-30 (2015). DOI: 10.1214/EJP.v20-3937

Abstract

The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing the Chebyshev polynomials of the first kind as the basis for the test function space. The covariance is explicitly computed and it is shown that for the Chebyshev polynomials of sufficiently high degree the covariance of linear statistics depends only on the first two moments of matrix entries.

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Vladislav Kargin. "Limit theorems for linear eigenvalue statistics of overlapping matrices." Electron. J. Probab. 20 1 - 30, 2015. https://doi.org/10.1214/EJP.v20-3937

Information

Received: 19 November 2014; Accepted: 6 November 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60013
MathSciNet: MR3425541
Digital Object Identifier: 10.1214/EJP.v20-3937

Subjects:
Primary: 60B20

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