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.
引用
收藏
页数：6
相关论文
共 50 条
  • [41] Jacobi sequences of squares of random variables
    Accardi, Luigi
    Barhoumi, Abdessatar
    Rhaima, Mohamed
    STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC REPORTS, 2017, 89 (6-7): : 868 - 882
  • [42] Jacobi sequences of powers of random variables
    Accardi, Luigi
    Barhoumi, Abdessatar
    Rhaima, Mohamed
    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2018, 21 (01)
  • [43] Characteristic Polynomials of Complex Random Matrices and Painleve Transcendents
    Deano, Alfredo
    Simm, Nick
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (01) : 210 - 264
  • [44] Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble
    Lyu, Shulin
    Min, Chao
    Chen, Yang
    JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (06)
  • [45] On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble
    Atkin, Max R.
    Charlier, Christophe
    Zohren, Stefan
    NONLINEARITY, 2018, 31 (04) : 1155 - 1196
  • [46] Critical Edge Behavior and the Bessel to Airy Transition in the Singularly Perturbed Laguerre Unitary Ensemble
    Xu, Shuai-Xia
    Dai, Dan
    Zhao, Yu-Qiu
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 332 (03) : 1257 - 1296
  • [47] Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painleve II and IV systems
    Lyu, Shulin
    Chen, Yang
    STUDIES IN APPLIED MATHEMATICS, 2021, 146 (01) : 118 - 138
  • [48] A centerless representation of the Virasoro algebra associated with the unitary circular ensemble
    Haine, Luc
    Vanderstichelen, Didier
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 236 (01) : 19 - 27
  • [49] ON THE CONDITION NUMBER OF THE CRITICALLY-SCALED LAGUERRE UNITARY ENSEMBLE
    Deift, Percy A.
    Trogdon, Thomas
    Menon, Govind
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (08) : 4287 - 4347
  • [50] The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble
    Lyu, Shulin
    Griffin, James
    Chen, Yang
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2019, 26 (01) : 24 - 53
12345