Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations

DOI10.1007/978-3-030-36744-2_22zbMath1443.33028arXiv1904.07518OpenAlexW2937295267MaRDI QIDQ3298088

Walter Van Assche

Publication date: 21 July 2020

Published in: Orthogonal Polynomials (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07518

zbMATH Keywords

orthogonal polynomialsrandom matricesPainlevé equationsmultiple orthogonal polynomials

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) 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) Painlevé-type functions (33E17)

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Orthogonal polynomials, Toda lattices and Painlevé equations ⋮ Planar orthogonal polynomials as type I multiple orthogonal polynomials ⋮ Asymptotics of discrete q-Freud II orthogonal polynomials from the q-Riemann Hilbert problem ⋮ On the quasi-orthogonality and Hahn-classicald-orthogonal polynomials ⋮ On the convergence of multi-level Hermite-Padé approximants for a class of meromorphic functions ⋮ Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series ⋮ Global fluctuations for multiple orthogonal polynomial ensembles ⋮ Multiple orthogonal polynomials: Pearson equations and Christoffel formulas ⋮ Asymptotics of the inertia moments and the variance conjecture in Schatten balls

Cites Work

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• Recurrence coefficients of a new generalization of the Meixner polynomials
• Nikishin systems are perfect
• Orthogonal polynomials on a bi-lattice
• Nearest neighbor recurrence relations for multiple orthogonal polynomials
• Coincidence probabilities
• Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions
• Nonnegative solutions of a nonlinear recurrence
• Discrete Painlevé equations and their appearance in quantum gravity
• Multiple orthogonal polynomials
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Random unitary matrices, permutations and Painlevé
• A Christoffel--Darboux formula for multiple orthogonal polynomials
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• Integral representations for multiple Hermite and multiple Laguerre polynomials.
• A differential equation for orthogonal polynomials
• UNITARY MATRIX MODELS AND PAINLEVÉ III
• WHAT IS...A Multiple Orthogonal Polynomial?
• Geometric aspects of Painlevé equations
• Asymptotic Expansions of Ratios of Coefficients of Orthogonal Polynomials with Exponential Weights
• Multiple orthogonal polynomial ensembles
• An Introduction to Random Matrices
• On the Toda Lattice. II: Inverse-Scattering Solution
• The Toda lattice. II. Existence of integrals
• Orthogonal Polynomials and Painlevé Equations
• Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations
• Analysis of Non-Linear Recurrence Relations for the Recurrence Coefficients of Generalized Charlier Polynomials
• Painlevé V and time-dependent Jacobi polynomials