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 |
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| Format: | Article |
| Language: | English |
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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| _version_ | 1862639009505738752 |
|---|---|
| author | Vasilchuk, V. |
| author_facet | Vasilchuk, V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | 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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| first_indexed | 2025-12-01T00:20:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106636 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-01T00:20:31Z |
| publishDate | 2010 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Vasilchuk, V. 2016-10-01T15:11:07Z 2016-10-01T15:11:07Z 2010 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. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106636 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 → ∞. 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands Article published earlier |
| spellingShingle | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands Vasilchuk, V. |
| title | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands |
| title_full | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands |
| title_fullStr | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands |
| title_full_unstemmed | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands |
| title_short | On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands |
| title_sort | on the law of addition of random matrices: covariance of traces of resolvent for random summands |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106636 |
| work_keys_str_mv | AT vasilchukv onthelawofadditionofrandommatricescovarianceoftracesofresolventforrandomsummands |