Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight | |
Min C.1; Chen Y.2![]() | |
2019-01-15 | |
Source Publication | Mathematical Methods in the Applied Sciences
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ISSN | 10991476 01704214 |
Volume | 42Issue: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. |
Keyword | Asymptotics Hankel Determinants Ladder Operators Orthogonal Polynomials Painlevé Transcendents Random Matrices |
DOI | https://doi.org/10.1002/mma.5347 |
URL | View the original |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000453074100020 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Affiliation | 1.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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