On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2014
• Main Author: Vasilchuk, V.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106809
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups / V. Vasilchuk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 4. — С. 451-484. — Бібліогр.: 9 назв. — англ.

We consider first the n x n random matrices Hn = An +Un*BnUn, where An and Bn are Hermitian, having the limiting normalized counting measure (NCM) of eigenvalues as n →∞, and Un is unitary uniformly distributed over U(n). We find the leading term of asymptotic expansion for the covariance of element...