Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities

DOI10.1007/s13324-021-00560-xzbMath1472.37062OpenAlexW3175065973MaRDI QIDQ1981645

Yang Chen, Mengkun Zhu, Dan Wang

Publication date: 6 September 2021

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-021-00560-x

zbMATH Keywords

asymptoticsorthogonal polynomialsPainlevé equationsladder operatorsLaguerre unitary ensembles

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52) Painlevé-type functions (33E17) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items (1)

Asymptotic relations for semi-classical Laguerre orthogonal polynomials and the associated Hankel determinants

Uses Software

• DLMF

Cites Work

• The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Fredholm determinants, differential equations and matrix models
• Painlevé differential equations in the complex plane
• Painlevé V for a Jacobi unitary ensemble with random singularities
• The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
• Painlevé V and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles
• Ladder operators and differential equations for orthogonal polynomials
• Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions
• Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling
• The recurrence coefficients of a semi-classical Laguerre polynomials and the large n asymptotics of the associated Hankel determinant
• Orthogonal polynomials with discontinuous weights
• Jacobi polynomials from compatibility conditions
• Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble
• On semiclassical orthogonal polynomials associated with a Freud‐type weixght
• Orthogonal polynomials, bi-confluent Heun equations and semi-classical weights
• On properties of a deformed Freud weight
• Orthogonal polynomials, asymptotics, and Heun equations
• Painlevé IV, σ-form, and the deformed Hermite unitary ensembles
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities