The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type

DOI10.3842/SIGMA.2018.076zbMath1396.34056arXiv1801.08740MaRDI QIDQ1654172

Mattia Cafasso, Manuel D. De La Iglesia

Publication date: 7 August 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.08740

zbMATH Keywords

Painlevé equationsToda latticesRiemann-Hilbert problemsmatrix-valued orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (6)

Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations ⋮ Asymptotics of matrix valued orthogonal polynomials on \([-1, 1\)] ⋮ Non-Abelian Toda-type equations and matrix valued orthogonal polynomials ⋮ Laguerre ensemble: correlators, Hurwitz numbers and Hodge integrals ⋮ The matrix Toda equations for coefficients of a matrix three-term recurrence relation ⋮ Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis

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