|
Журнал математической физики, анализа, геометрии, 2013, том 9, номер 4, страницы 536–581
(Mi jmag579)
|
|
|
|
Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
On Non-Gaussian Limiting Laws for Certain Statistics of Wigner Matrices
A. Lytova B. Verkin Institute for Low Temperature Physics and Engineering,
National Academy of Sciences of Ukraine,
47 Lenin Ave., Kharkiv 61103, Ukraine
Аннотация:
This paper is a continuation of our papers [12–14] in which the limiting laws of fluctuations were found for the linear eigenvalue statistics $\mathrm{Tr}\,\varphi (M^{(n)})$ and for the normalized matrix elements $\sqrt{n}\varphi_{jj}(M^{(n)})$ of differentiable functions of real symmetric Wigner matrices $M^{(n)}$ as $n\rightarrow\infty$. Here we consider another spectral characteristic of Wigner matrices, $\xi^{A} _{n}[\varphi ]=\mathrm{Tr}\,\varphi (M^{(n)})A^{(n)}$, where $\{A^{(n)}\}_{n=1}^\infty$ is a certain sequence of non-random matrices. We show first that if $M^{(n)}$ belongs to the Gaussian Orthogonal Ensemble, then $\xi^{A} _{n}[\varphi ]$ satisfies the Central Limit Theorem. Then we consider Wigner matrices with i.i.d. entries possessing the entire characteristic function and find the limiting probability law for $\xi^{A} _{n}[\varphi ]$, which in general is not Gaussian.
Ключевые слова и фразы:
Wigner matrices, spectral characteristics, central limit theorem.
Поступила в редакцию: 02.04.2012
Образец цитирования:
A. Lytova, “On Non-Gaussian Limiting Laws for Certain Statistics of Wigner Matrices”, Журн. матем. физ., анал., геом., 9:4 (2013), 536–581
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag579 https://www.mathnet.ru/rus/jmag/v9/i4/p536
|
Статистика просмотров: |
Страница аннотации: | 266 | PDF полного текста: | 62 | Список литературы: | 47 |
|