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Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight
Min C.1; Chen Y.2
2019-01-15
Source PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214
Volume42Issue:1Pages:301-321
Abstract

This paper studies the Hankel determinants generated by a discontinuous Gaussian weight with one and two jumps. It is an extension in a previous study, in which they studied the discontinuous Gaussian weight with a single jump. By using the ladder operator approach, we obtain a series of difference and differential equations to describe the Hankel determinant for the single jump case. These equations include the Chazy II equation, continuous and discrete Painlevé IV. In addition, we consider the large n behavior of the corresponding orthogonal polynomials and prove that they satisfy the biconfluent Heun equation. We also consider the jump at the edge under a double scaling, from which a Painlevé XXXIV appeared. Furthermore, we study the Gaussian weight with two jumps and show that a quantity related to the Hankel determinant satisfies a two variables' generalization of the Jimbo-Miwa-Okamoto σ-form of the Painlevé IV.

KeywordAsymptotics Hankel Determinants Ladder Operators Orthogonal Polynomials Painlevé Transcendents Random Matrices
DOIhttps://doi.org/10.1002/mma.5347
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000453074100020
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.School of Mathematical Sciences, Huaqiao University, Quanzhou, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Taipa, Macau, China
Recommended Citation
GB/T 7714
Min C.,Chen Y.. Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight[J]. Mathematical Methods in the Applied Sciences,2019,42(1):301-321.
APA Min C.,&Chen Y..(2019).Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight.Mathematical Methods in the Applied Sciences,42(1),301-321.
MLA Min C.,et al."Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight".Mathematical Methods in the Applied Sciences 42.1(2019):301-321.
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