PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE

DOI10.1142/S2010326311500031zbMath1288.60003arXiv1102.0402OpenAlexW2962678341MaRDI QIDQ2893153

Lun Zhang, Estelle L. Basor, Yang Chen

Publication date: 26 June 2012

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0402

zbMATH Keywords

orthogonal polynomialsPainlevé equationsladder operatorsHermitian random matricesextreme eigenvalues distributions

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Painlevé-type functions (33E17)

Related Items (13)

The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble ⋮ On a distinguished family of random variables and Painlevé equations ⋮ Hankel determinants for a Gaussian weight with Fisher–Hartwig singularities and generalized Painlevé IV equation ⋮ Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble ⋮ Approximation of rectangular beta-Laguerre ensembles and large deviations ⋮ 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 ⋮ Random matrix models, double-time Painlevé equations, and wireless relaying ⋮ Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight ⋮ Perturbed Laguerre unitary ensembles, Hankel determinants, and information theory ⋮ Large complex correlated Wishart matrices: fluctuations and asymptotic independence at the edges ⋮ On the condition number of the critically-scaled Laguerre unitary ensemble

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