Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling

DOI10.1111/sapm.12198zbMath1388.60030arXiv1803.10954OpenAlexW2768484945MaRDI QIDQ4564864

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Publication date: 7 June 2018

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

Full work available at URL: https://arxiv.org/abs/1803.10954

zbMATH Keywords

Jacobi unitary ensembleHermitian random matricesPainlevé V equationJimbo-Miwa-Okamoto \(\sigma\) form

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52)

Related Items (11)

Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues ⋮ The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble ⋮ Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble ⋮ Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles ⋮ Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system ⋮ Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight ⋮ Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities ⋮ On determinant expansions for Hankel operators ⋮ Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight ⋮ Orthogonal polynomials, asymptotics, and Heun equations ⋮ Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble

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