Residential Collegefalse
The hankel determinants from a singularly perturbed jacobi weight
Han, Pengju1; Chen, Yang2
Source PublicationMathematics
AbstractWe study the Hankel determinant generated by a singularly perturbed Jacobi weight (Formula presented). If s = 0, it is reduced to the classical Jacobi weight. For s > 0, the factor (Formula presented) induces an infinitely strong zero at x = 1. For the finite n case, we obtain four auxiliary quantities R (s), r (s), ˜R (s), and ˜r (s) by using the ladder operator approach. We show that the recurrence coefficients are expressed in terms of the four auxiliary quantities with the aid of the compatibility conditions. Furthermore, we derive a shifted Jimbo–Miwa–Okamoto σ-function of a particular Painlevé V for the logarithmic derivative of the Hankel determinant D (s). By variable substitution and some complicated calculations, we show that the quantity R (s) satisfies the four Painlevé equations. For the large n case, we show that, under a double scaling, where n tends to ∞ and s tends to 0, such that τ:= n s is finite, the scaled Hankel determinant can be expressed by a particular P.
KeywordHankel determinant Ladder operators Painlevé V Random matrix theory Singularly perturbed Jacobi weight
URLView the original
Scopus ID2-s2.0-85119931129
Fulltext Access
Citation statistics
Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.College of Science, Huazhong Agricultural University, Wuhan, 430070, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, 999078, Macao
Recommended Citation
GB/T 7714
Han, Pengju,Chen, Yang. The hankel determinants from a singularly perturbed jacobi weight[J]. Mathematics,2021,9(22).
APA Han, Pengju,&Chen, Yang.(2021).The hankel determinants from a singularly perturbed jacobi weight.Mathematics,9(22).
MLA Han, Pengju,et al."The hankel determinants from a singularly perturbed jacobi weight".Mathematics 9.22(2021).
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Han, Pengju]'s Articles
[Chen, Yang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Han, Pengju]'s Articles
[Chen, Yang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Han, Pengju]'s Articles
[Chen, Yang]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.