On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups

We consider first the n x n random matrices Hn = An +Un*BnUn, where An and Bn are Hermitian, having the limiting normalized counting measure (NCM) of eigenvalues as n →∞, and Un is unitary uniformly distributed over U(n). We find the leading term of asymptotic expansion for the covariance of element...

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Дата:	2014
Автор:	Vasilchuk, V.
Формат:	Стаття
Мова:	English
Опубліковано:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2014
Назва видання:	Журнал математической физики, анализа, геометрии
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/106809
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups / V. Vasilchuk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 4. — С. 451-484. — Бібліогр.: 9 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-106809
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spelling	irk-123456789-1068092016-10-06T03:02:31Z On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups Vasilchuk, V. We consider first the n x n random matrices Hn = An +UnBnUn, where An and Bn are Hermitian, having the limiting normalized counting measure (NCM) of eigenvalues as n →∞, and Un is unitary uniformly distributed over U(n). We find the leading term of asymptotic expansion for the covariance of elements of resolvent of Hn and establish the Central Limit Theorem for the elements of suffciently smooth test functions of the corresponding linear statistics. We consider then analogous problems for the matrices Wn = SnUnTnUn, where Un is as above and Sn and Tn are non-random unitary matrices having limiting NCM's as n →∞. Рассмотрены сначала n x n случайные матрицы вида Hn = An +UnBnUn, где An и Bn - эрмитовы, имеющие предельную нормированную считающую меру (НСМ) собственных значений при n →∞, и Un - унитарные, распределенные равномерно по U(n). Найден ведущий член асимптотического разложения ковариации элементов резольвенты Hn и доказана Центральная Предельная Теорема для элементов достаточно гладких тестовых функций соответствующих линейных статистик. Затем аналогичные задачи рассмотрены для матриц вида Wn = SnUnTnUn, где Un такая же, а Sn и Tn - неслучайные унитарные матрицы, имеющие предельные НСМ n →∞. 2014 Article On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups / V. Vasilchuk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 4. — С. 451-484. — Бібліогр.: 9 назв. — англ. 1812-9471 DOI: http://dx.doi.org/10.15407/mag10.04.451 http://dspace.nbuv.gov.ua/handle/123456789/106809 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 first the n x n random matrices Hn = An +UnBnUn, where An and Bn are Hermitian, having the limiting normalized counting measure (NCM) of eigenvalues as n →∞, and Un is unitary uniformly distributed over U(n). We find the leading term of asymptotic expansion for the covariance of elements of resolvent of Hn and establish the Central Limit Theorem for the elements of suffciently smooth test functions of the corresponding linear statistics. We consider then analogous problems for the matrices Wn = SnUnTnUn, where Un is as above and Sn and Tn are non-random unitary matrices having limiting NCM's as n →∞.
format	Article
author	Vasilchuk, V.
spellingShingle	Vasilchuk, V. On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups Журнал математической физики, анализа, геометрии
author_facet	Vasilchuk, V.
author_sort	Vasilchuk, V.
title	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups
title_short	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups
title_full	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups
title_fullStr	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups
title_full_unstemmed	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups
title_sort	on the fluctuations of entries of matrices whose randomness is due to classical groups
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2014
url	http://dspace.nbuv.gov.ua/handle/123456789/106809
citation_txt	On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups / V. Vasilchuk // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 4. — С. 451-484. — Бібліогр.: 9 назв. — англ.
series	Журнал математической физики, анализа, геометрии
work_keys_str_mv	AT vasilchukv onthefluctuationsofentriesofmatriceswhoserandomnessisduetoclassicalgroups
first_indexed	2023-10-18T20:13:45Z
last_indexed	2023-10-18T20:13:45Z
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On the Fluctuations of Entries of Matrices whose Randomness is due to Classical Groups

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