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Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling
Min, Chao; Chen, Yang
2018-02
Source PublicationSTUDIES IN APPLIED MATHEMATICS
ISSN0022-2526
Volume140Issue:2Pages:202-220
AbstractIn 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
Citation statistics
Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Recommended Citation
GB/T 7714
Min, Chao,Chen, Yang. Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling[J]. STUDIES IN APPLIED MATHEMATICS,2018,140(2):202-220.
APA Min, Chao,&Chen, Yang.(2018).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 Min, Chao,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(2018):202-220.
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