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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| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106636 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106636 |
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dspace |
| spelling |
irk-123456789-1066362016-10-02T03:02:43Z On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands Vasilchuk, V. 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 → ∞. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106636 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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 → ∞. |
| format |
Article |
| author |
Vasilchuk, V. |
| spellingShingle |
Vasilchuk, V. On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands Журнал математической физики, анализа, геометрии |
| author_facet |
Vasilchuk, V. |
| author_sort |
Vasilchuk, V. |
| title |
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_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_sort |
on the law of addition of random matrices: covariance of traces of resolvent for random summands |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106636 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
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2023-10-18T20:13:22Z |
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2023-10-18T20:13:22Z |
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1796149294985641984 |