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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Опубліковано в: :Журнал математической физики, анализа, геометрии
Дата:2010
Автор: Vasilchuk, V.
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2010
Онлайн доступ:https://nasplib.isofts.kiev.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 nasplib_isofts_kiev_ua-123456789-106636
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands
spellingShingle On the Law of Addition of Random Matrices: Covariance of Traces of Resolvent for Random Summands
Vasilchuk, V.
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
author Vasilchuk, V.
author_facet Vasilchuk, V.
publishDate 2010
language English
container_title Журнал математической физики, анализа, геометрии
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
format Article
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 → ∞.
issn 1812-9471
url https://nasplib.isofts.kiev.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.
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