Riemann-Hilbert Problems, Matrix Orthogonal Polynomials and Discrete Matrix Equations with Singularity Confinement

DOI10.1111/j.1467-9590.2011.00541.xzbMath1246.33003arXiv1106.0036OpenAlexW3124187675MaRDI QIDQ2896006

Manuel Mañas, Giovanni A. Cassatella-Contra

Publication date: 13 July 2012

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

Full work available at URL: https://arxiv.org/abs/1106.0036

zbMATH Keywords

Riemann-Hilbert problemmatrix Freud casequartic Freud matrix orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

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Matrix-valued orthogonal polynomials related to hexagon tilings, Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations, Multivariate orthogonal polynomials and integrable systems, The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type, Riemann-Hilbert problem and matrix biorthogonal polynomials, Asymptotics of matrix valued orthogonal polynomials on \([-1, 1\)], Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems, Critical measures on higher genus Riemann surfaces, Matrix Jacobi biorthogonal polynomials via Riemann–Hilbert problem, Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective, Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach, The two-periodic Aztec diamond and matrix valued orthogonal polynomials, Nonlinear q-Stokes phenomena for q-Painlevé I, Painlevé type reductions for the non-Abelian Volterra lattices ^*

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