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Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling
Chao Min; Yang Chen
2017-11-22
Source PublicationSTUDIES IN APPLIED MATHEMATICS
ISSN0022-2526
Volume140Issue:2Pages:202-220
Abstract

In this paper, we study the gap probability problem of the (symmetric) Jacobi unitary ensemble of Hermitian random matrices, namely, the probability that the interval (-a, a) (0 < a < 1) is free of eigenvalues. Using the ladder operator technique for orthogonal polynomials and the associated supplementary conditions, we derive three quantities instrumental in the gap probability, denoted by H-n(a), R-n(a), and r(n)(a). We find that each one satisfies a second-order differential equation. We show that after a double scaling, the large second-order differential equation in the variable a with n as parameter satisfied by H-n(a) can be reduced to the Jimbo-MiwaOkamoto sigma form of the Painleve V equation.

DOI10.1111/sapm.12198
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000424115400003
PublisherWILEY
The Source to ArticleWOS
Fulltext Access
Citation statistics
Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorYang Chen
AffiliationDepartment of Mathematics, University of Macau, Avenidada Universidade, Taipa, Macau, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Chao Min,Yang Chen. Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling[J]. STUDIES IN APPLIED MATHEMATICS,2017,140(2):202-220.
APA Chao Min,&Yang Chen.(2017).Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling.STUDIES IN APPLIED MATHEMATICS,140(2),202-220.
MLA Chao Min,et al."Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling".STUDIES IN APPLIED MATHEMATICS 140.2(2017):202-220.
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