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On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands
Репозиторій DSpace/Manakin
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On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands
Посилання:
On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands / V. Vasilchuk // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 96-127. — Бібліогр.: 18 назв. — англ.
Підтримка:
This work was supported by Franco-Ukrainian programme PICS (2009{2011) of NAS of Ukraine and CNRS. The author is thankful to Prof L. Pastur for helpful discussions.
Дата:
2010
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629
Завантажень:
256
Анотація:
We consider the ensemble of n£n random matrices Hn = An+U†n BnUn, where An and Bn are random Hermitian (real symmetric) matrices, having the limiting Normalized Counting Measures of eigenvalues, and Un is unitary (orthogonal) uniformly distributed over U(n) (O(n)). We find the leading term of the asymptotic expansion of covariance of traces of resolvent of Hn and establish the Central Limit Theorem for linear eigenvalue statistics of Hn as n → ∞.
