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Painlevé III′ and the Hankel determinant generated by a singularly perturbed Gaussian weight
Min C.1; Lyu S.2; Chen Y.3
2018-11-01
Source PublicationNuclear Physics B
ISSN05503213
Volume936Pages:169-188
Abstract

In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weight w(x,t)=e,x∈(−∞,∞),t>0. By using the ladder operator approach associated with the orthogonal polynomials, we show that the logarithmic derivative of the Hankel determinant satisfies both a non-linear second order difference equation and a non-linear second order differential equation. The Hankel determinant also admits an integral representation involving a Painlevé III′. Furthermore, we consider the asymptotics of the Hankel determinant under a double scaling, i.e. n→∞ and t→0 such that s=(2n+1)t is fixed. The asymptotic expansions of the scaled Hankel determinant for large s and small s are established, from which Dyson's constant appears.

DOIhttps://doi.org/10.1016/j.nuclphysb.2018.09.016
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Particles & Fields
WOS IDWOS:000448811800009
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorChen Y.
Affiliation1.School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
2.School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China
3.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Min C.,Lyu S.,Chen Y.. Painlevé III′ and the Hankel determinant generated by a singularly perturbed Gaussian weight[J]. Nuclear Physics B,2018,936:169-188.
APA Min C.,Lyu S.,&Chen Y..(2018).Painlevé III′ and the Hankel determinant generated by a singularly perturbed Gaussian weight.Nuclear Physics B,936,169-188.
MLA Min C.,et al."Painlevé III′ and the Hankel determinant generated by a singularly perturbed Gaussian weight".Nuclear Physics B 936(2018):169-188.
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