UM
Painleve transcendents and the Hankel determinants generated by a discontinuous Gaussian weight
Min, Chao1; Chen, Yang2
2019-01-15
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Volume42Issue:1Pages:301-321
AbstractThis 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 Painleve 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 Painleve 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 sigma-form of the Painleve IV.
Keywordasymptotics Hankel determinants ladder operators orthogonal polynomials Painleve transcendents random matrices
DOI10.1002/mma.5347
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000453074100020
PublisherWILEY
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Huaqiao Univ, Sch Math Sci, Quanzhou, Peoples R China;
2.Univ Macau, Fac Sci & Technol, Dept Math, Ave Univ, Taipa, Macau, Peoples R China
Recommended Citation
GB/T 7714
Min, Chao,Chen, Yang. Painleve 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, Chao,&Chen, Yang.(2019).Painleve transcendents and the Hankel determinants generated by a discontinuous Gaussian weight.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,42(1),301-321.
MLA Min, Chao,et al."Painleve 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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