Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systems

DOI10.1111/sapm.12343zbMath1472.82002arXiv2006.07596OpenAlexW3116628095WikidataQ114078129 ScholiaQ114078129MaRDI QIDQ4995573

Yang Chen, Shu-Lin Lyu

Publication date: 25 June 2021

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

Full work available at URL: https://arxiv.org/abs/2006.07596

zbMATH Keywords

orthogonal polynomialsHankel determinantPainlevé equationsGaussian unitary ensembles

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Classical equilibrium statistical mechanics (general) (82B05) Random matrices (algebraic aspects) (15B52) Painlevé-type functions (33E17)

Related Items (6)

Truncated Hermite polynomials ⋮ Hankel determinants for a Gaussian weight with Fisher–Hartwig singularities and generalized Painlevé IV equation ⋮ A two-component Sasa-Satsuma equation: large-time asymptotics on the line ⋮ Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system ⋮ Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations ⋮ Exponential moments for disk counting statistics of random normal matrices in the critical regime

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