Painlevé IV Asymptotics for Orthogonal Polynomials with Respect to a Modified Laguerre Weight

DOI10.1111/j.1467-9590.2008.00423.xzbMath1189.33014arXiv0804.2564OpenAlexW2963640992MaRDI QIDQ3393019

Dan Dai, Arno B. J. Kuijlaars

Publication date: 18 August 2009

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.2564

zbMATH Keywords

Painlevé IV equationorthogonal polynomialmodified Laguerre weight

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (16)

Painlevé III Asymptotics of Hankel Determinants for a Perturbed Jacobi Weight ⋮ Riemann-Hilbert problem and matrix biorthogonal polynomials ⋮ Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane ⋮ Discontinuity in the asymptotic behavior of planar orthogonal polynomials under a perturbation of the Gaussian weight ⋮ Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena ⋮ The Szegő curve and Laguerre polynomials with large negative parameters ⋮ Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system ⋮ Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective ⋮ On integrable Ermakov-Painlevé IV systems ⋮ Critical edge behavior in the modified Jacobi ensemble and the Painlevé V transcendents ⋮ Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach ⋮ On tronquée solutions of the first Painlevé hierarchy ⋮ Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy ⋮ Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane ⋮ Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge ⋮ Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Self-similar solutions of the modified nonlinear Schrödinger equation
• Monodromy- and spectrum-preserving deformations. I
• The isomonodromy approach to matrix models in 2D quantum gravity
• Level-spacing distributions and the Airy kernel
• Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter.
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Universality of a double scaling limit near singular edge points in random matrix models
• Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight
• Universality of the double scaling limit in random matrix models
• Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painlevé Transcendent
• On the distribution of the length of the longest increasing subsequence of random permutations
• Solutions of the second and fourth Painlevé equations, I
• Double scaling limit in the random matrix model: The Riemann-Hilbert approach
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation
• On Painlevé's equations I, II and IV

This page was built for publication: Painlevé IV Asymptotics for Orthogonal Polynomials with Respect to a Modified Laguerre Weight