Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2011
• Main Author: Shcherbina, M.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106671
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...