Perturbed Hankel determinant, correlation functions and Painlevé equations

DOI10.1063/1.4939276zbMath1338.33020arXiv1507.05261OpenAlexW2208490835MaRDI QIDQ2795581

Min Chen, Yang Chen, En-gui Fan

Publication date: 21 March 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05261

zbMATH Keywords

Hankel determinantHankel matrixBessel differential equation

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) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Linear transformations, semilinear transformations (15A04)

Related Items (9)

Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues ⋮ Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight ⋮ The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble ⋮ Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble ⋮ Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles ⋮ Single-user MIMO system, Painlevé transcendents, and double scaling ⋮ Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight ⋮ Orthogonal polynomials, asymptotics, and Heun equations ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation

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