Zero distribution of complex orthogonal polynomials with respect to exponential weights

DOI10.1016/j.jat.2014.05.002zbMath1297.42037arXiv1312.4376OpenAlexW2016659803WikidataQ117717441 ScholiaQ117717441MaRDI QIDQ2016133

Nele Lejon, Daan Huybrechs, Arno B. J. Kuijlaars

Publication date: 19 June 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4376

zbMATH Keywords

logarithmic potentialdistribution of zerosexternal fieldcomplex orthogonal polynomialsanalytic arcvarying weightnon-Hermitian inner-product

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation in the complex plane (30E10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (11)

Investigation of the two-cut phase region in the complex cubic ensemble of random matrices ⋮ Matrix-valued orthogonal polynomials related to hexagon tilings ⋮ Convergence to equilibrium in the free Fokker-Planck equation with a double-well potential ⋮ Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval ⋮ The Mother Body Phase Transition in the Normal Matrix Model ⋮ Openness of regular regimes of complex random matrix models ⋮ Nonintersecting Brownian bridges on the unit circle with drift ⋮ Topological expansion in the complex cubic log-gas model: one-cut case ⋮ S-curves in polynomial external fields ⋮ The \(k\)-tacnode process ⋮ Phase structure and asymptotic zero densities of orthogonal polynomials in the cubic model

Cites Work

• Unnamed Item
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• Unnamed Item
• Superpotentials, quantum parameter space and phase transitions in \( \mathcal{N}=1\) supersymmetric gauge theories
• Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters
• Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
• Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials
• Boutroux curves with external field: equilibrium measures without a variational problem
• Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights
• Complex Gaussian quadrature of oscillatory integrals
• S-curves in polynomial external fields
• Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation
• On the Grunsky inequalities for univalent functions
• Spectral curves in gauge/string dualities: integrability, singular sectors and regularization
• Variation of the equilibrium energy and theS-property of stationary compact sets
• Determination ofS-curves with applications to the theory of non-Hermitian orthogonal polynomials
• EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS
• Orthogonal Polynomials and 𝑆-curves

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