Affiliated with RC | false |
Status | 已發表Published |
Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities | |
Zhu, Mengkun1,2; Wang, Dan2; Chen, Yang2 | |
2021-09-01 | |
Source Publication | Analysis and Mathematical Physics |
ISSN | 1664-2368 |
Volume | 11Issue:3 |
Abstract | In this paper, we present the characteristic of a certain discontinuous linear statistic of the semi-classical Laguerre unitary ensembles w(z,t)=Aθ(z-t)e-z2+tz,here θ(x) is the Heaviside function, where A> 0 , t> 0 , and z∈ [0 , ∞). We derive the ladder operators and its interrelated compatibility conditions. By using the ladder operators, we show two auxiliary quantities R(t) and r(t) satisfy the coupled Riccati equations, from which we also prove that R(t) satisfies a particular Painlevé IV equation. Even more, σ(t) , allied to R(t) , satisfies both the discrete and continuous Jimbo–Miwa–Okamoto σ-form of the Painlevé IV equation. Finally, we consider the situation when n gets large, the second order linear differential equation satisfied by the polynomials P(x) orthogonal with respect to the semi-classical weight turn to be a particular bi-confluent Heun equation. |
Keyword | Asymptotics Ladder Operators Laguerre Unitary Ensembles Orthogonal Polynomials Painlevé Equations |
DOI | 10.1007/s13324-021-00560-x |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000667679300001 |
Scopus ID | 2-s2.0-85108970374 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Wang, Dan; Chen, Yang |
Affiliation | 1.School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China 2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Avenida da Universidade, Macao |
First Author Affilication | Faculty of Science and Technology |
Corresponding Author Affilication | Faculty of Science and Technology |
Recommended Citation GB/T 7714 | Zhu, Mengkun,Wang, Dan,Chen, Yang. Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities[J]. Analysis and Mathematical Physics,2021,11(3). |
APA | Zhu, Mengkun,Wang, Dan,&Chen, Yang.(2021).Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities.Analysis and Mathematical Physics,11(3). |
MLA | Zhu, Mengkun,et al."Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities".Analysis and Mathematical Physics 11.3(2021). |
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