UM  > Faculty of Science and Technology  > DEPARTMENT OF MATHEMATICS
Linear statistics of matrix ensembles in classical background
Min C.; Chen Y.
Source PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214

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(·). 

KeywordAsymptotics Linear Spectral Statistics Orthogonal Polynomials Random Matrices
URLView the original
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000384078300017
Fulltext Access
Citation statistics
Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
AffiliationDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
First Author AffilicationUniversity 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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Min C.]'s Articles
[Chen Y.]'s Articles
Baidu academic
Similar articles in Baidu academic
[Min C.]'s Articles
[Chen Y.]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Min C.]'s Articles
[Chen Y.]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.