Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane

DOI10.3842/SIGMA.2018.091zbMath1400.33008arXiv1802.01153OpenAlexW2785991169MaRDI QIDQ1792495

José Gustavo Elias Rebelo, Marco Bertola, Tamara Grava

Publication date: 12 October 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/1802.01153

zbMATH Keywords

Riemann-Hilbert problemorthogonal polynomials on the complex planePainlevé equations Fredholm determinant

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Special function solutions of Painlevé equations: theory, asymptotics and applications ⋮ Asymptotics of determinants with a rotation-invariant weight and discontinuities along circles ⋮ Planar orthogonal polynomials as type I multiple orthogonal polynomials ⋮ Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges ⋮ Determinantal Coulomb Gas Ensembles with a Class of Discrete Rotational Symmetric Potentials ⋮ The planar low temperature Coulomb gas: separation and equidistribution ⋮ The random normal matrix model: insertion of a point charge ⋮ Exponential moments for disk counting statistics at the hard edge of random normal matrices ⋮ Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena ⋮ Szegő type asymptotics for the reproducing kernel in spaces of full-plane weighted polynomials ⋮ Scaling limits of random normal matrix processes at singular boundary points ⋮ The τ-function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant ⋮ Scaling limits of planar symplectic ensembles ⋮ Fredholm determinant representation of the homogeneous Painlevé II τ-function ⋮ Exponential moments for disk counting statistics of random normal matrices in the critical regime

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