Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
|
| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106671 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices / M. Shcherbina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 176-192. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106671 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1066712016-10-02T03:03:06Z Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices Shcherbina, M. We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions and also on the number of the entries moments. Moreover, we develop a universal method which allows one to obtain automatically the bounds for the variance of differentiable test functions, if there is a bound for the variance of the trace of the resolvent of random matrix. The method is applicable not only to the Wigner and sample covariance matrices, but to any ensemble of hermitian or real symmetric random matrices. 2011 Article Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices / M. Shcherbina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 176-192. — Бібліогр.: 15 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106671 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 two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions and also on the number of the entries moments. Moreover, we develop a universal method which allows one to obtain automatically the bounds for the variance of differentiable test functions, if there is a bound for the variance of the trace of the resolvent of random matrix. The method is applicable not only to the Wigner and sample covariance matrices, but to any ensemble of hermitian or real symmetric random matrices. |
| format |
Article |
| author |
Shcherbina, M. |
| spellingShingle |
Shcherbina, M. Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices Журнал математической физики, анализа, геометрии |
| author_facet |
Shcherbina, M. |
| author_sort |
Shcherbina, M. |
| title |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices |
| title_short |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices |
| title_full |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices |
| title_fullStr |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices |
| title_full_unstemmed |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices |
| title_sort |
central limit theorem for linear eigenvalue statistics of the wigner and sample covariance random matrices |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106671 |
| citation_txt |
Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices / M. Shcherbina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 2. — С. 176-192. — Бібліогр.: 15 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT shcherbinam centrallimittheoremforlineareigenvaluestatisticsofthewignerandsamplecovariancerandommatrices |
| first_indexed |
2023-10-18T20:13:27Z |
| last_indexed |
2023-10-18T20:13:27Z |
| _version_ |
1796149298137661440 |