Painleve V for a Jacobi unitary ensemble with random singularities

被引：6
作者：
Zhu, Mengkun [1 ,2 ]
Li, Chuanzhong [3 ,4 ]
Chen, Yang [2 ]
机构：
[1] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Peoples R China
[2] Univ Macau, Dept Math, Ave Univ, Taipa, Macau, Peoples R China
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[4] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2021年 / 120卷
基金：
中国国家自然科学基金;
关键词：
Jacobi unitary ensembles; Orthogonal polynomials; Painleve V; Ladder operators; DIFFERENTIAL-EQUATIONS;
D O I：
10.1016/j.aml.2021.107242
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we focus on the relationship between the fifth Painleve equation and a Jacobi weight perturbed with random singularities, w(z) = (1 - z(2))(alpha) e(-t/z2-k2), z, k is an element of [-1, 1], alpha, t > 0. By using the ladder operator approach, we obtain that an auxiliary quantity R-n(t), which is closely related to the recurrence coefficients of monic polynomials orthogonal with w(z), satisfies a particular Painleve V equation. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：6
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