On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands
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 as...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2010 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106636 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 → ∞.
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| ISSN: | 1812-9471 |