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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2011, Volume 7, Number 2, Pages 176–192
(Mi jmag511)
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This article is cited in 53 scientific papers (total in 53 papers)
Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
M. Shcherbina Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
Abstract:
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions and also on the number of the entries moments. Moreover, we develop a universal method which allows one to obtain automatically the bounds for the variance of differentiable test functions, if there is a bound for the variance of the trace of the resolvent of random matrix. The method is applicable not only to the Wigner and sample covariance matrices, but to any ensemble of hermitian or real symmetric random matrices.
Key words and phrases:
random matrices, Wigner matrix, sample covariance matrix, Central Limit Theorem.
Received: 20.01.2010
Citation:
M. Shcherbina, “Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices”, Zh. Mat. Fiz. Anal. Geom., 7:2 (2011), 176–192
Linking options:
https://www.mathnet.ru/eng/jmag511 https://www.mathnet.ru/eng/jmag/v7/i2/p176
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Abstract page: | 518 | Full-text PDF : | 135 | References: | 62 |
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