Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices
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| Creator |
Shcherbina, M.
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| Description |
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.
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| Date |
2016-10-01T19:29:56Z
2016-10-01T19:29:56Z 2011 |
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| Type |
Article
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| Identifier |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices / M. Shcherbina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 176-192. — Бібліогр.: 15 назв. — англ.
1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106671 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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