Universality limits involving orthogonal polynomials on the unit circle

DOI10.1007/BF03321662zbMath1214.42045OpenAlexW2065839073MaRDI QIDQ925174

Eli Levin, Doron S. Lubinsky

Publication date: 30 May 2008

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321662

zbMATH Keywords

universality limits

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Polynomials and rational functions of one complex variable (30C10)

Related Items (18)

An update on local universality limits for correlation functions generated by unitary ensembles ⋮ Universality limits involving orthogonal polynomials on an arc of the unit circle ⋮ Some recent methods for establishing universality limits ⋮ On the spacing of zeros of paraorthogonal polynomials for singular measures ⋮ A new linear spectral transformation associated with derivatives of Dirac linear functionals ⋮ Universality limits in the bulk for varying measures ⋮ Two universality results for polynomial reproducing kernels ⋮ Local asymptotics for orthonormal polynomials on the unit circle via universality ⋮ Zeros of random orthogonal polynomials with complex Gaussian coefficients ⋮ Universality type limits for Bergman orthogonal polynomials ⋮ On Some Recent Results on Asymptotic Behavior of Orthogonal Polynomials on the Unit Circle and Inserting Point Masses ⋮ Universality limits in the bulk for arbitrary measures on compact sets ⋮ Ewens Measures on Compact Groups and Hypergeometric Kernels ⋮ Universality limits for random matrices and de Branges spaces of entire functions ⋮ Applications of a new formula for OPUC with periodic Verblunsky coefficients ⋮ Zeros of real random polynomials spanned by OPUC ⋮ DISCRETE CIRCULAR BETA ENSEMBLES ⋮ \(L_p\) Christoffel functions, \(L_p\) universality, and Paley-Wiener spaces

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• Szegö's extremum problem on the unit circle
• Akhiezer's orthogonal polynomials and Bernstein-Szegő method for a circular arc
• Asymptotics for Christoffel functions for general measures on the real line
• Universality limits for exponential weights
• First and second kind paraorthogonal polynomials and their zeros
• Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials
• The Formula steepest descent method and the asymptotic behavior of polynomials orthogonal on the unit circle with fixed and exponentially varying nonanalytic weights
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior
• \(L_p\) Markov-Bernstein inequalities on arcs of the circle

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