Linear statistics of matrix ensembles in classical background | |
Min C.; Chen Y. | |
2016-09-15 | |
Source Publication | Mathematical Methods in the Applied Sciences |
ISSN | 10991476 01704214 |
Volume | 39Issue:13Pages:3758-3790 |
Abstract | Given a joint probability density function of N real random variables, (X) , obtained from the eigenvector–eigenvalue decomposition of N × N random matrices, one constructs a random variable, the linear statistics, defined by the sum of smooth functions evaluated at the eigenvalues or singular values of the random matrix, namely, ∑ F(X). For the joint PDFs obtained from the Gaussian and Laguerre ensembles, we compute, in this paper, the moment-generating function E, where (-λ ∑ F(x)) where E denotes expectation value over the orthogonal (β = 1) and symplectic (β = 4) ensembles, in the form one plus a Schwartz function, none vanishing over ℝ for the Gaussian ensembles and ℝ for the Laguerre ensembles. These are ultimately expressed in the form of the determinants of identity plus a scalar operator, from which we obtained the large N asymptotic of the linear statistics from suitably scaled F(·). |
Keyword | Asymptotics Linear Spectral Statistics Orthogonal Polynomials Random Matrices |
DOI | https://doi.org/10.1002/mma.3824 |
URL | View the original |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000384078300017 |
Publisher | WILEY-BLACKWELL, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Affiliation | Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China |
First Author Affilication | University of Macau |
Recommended Citation GB/T 7714 | Min C.,Chen Y.. Linear statistics of matrix ensembles in classical background[J]. Mathematical Methods in the Applied Sciences,2016,39(13):3758-3790. |
APA | Min C.,&Chen Y..(2016).Linear statistics of matrix ensembles in classical background.Mathematical Methods in the Applied Sciences,39(13),3758-3790. |
MLA | Min C.,et al."Linear statistics of matrix ensembles in classical background".Mathematical Methods in the Applied Sciences 39.13(2016):3758-3790. |
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