Painlevé V for a Jacobi unitary ensemble with random singularities

2021/03/13 by Mengkun Zhu, Zhu, Mengkun, Chuanzhong Li +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2103.07816

openalex publication_date 2021/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper, we focus on the relationship between the fifth Painlevé equation and a Jacobi weight perturbed with random singularities, w(z)=(1-z²)^α\rm e^-(t)/(z2-k2),~~~z,k∈[-1,1],~α,tgt;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 Painlevé V equation.

Citations

• Ladder operators and differential equations for orthogonal polynomials
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles, I
• Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials

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