Random Matrix Ensembles with Singularities and a Hierarchy of Painlevé III Equations

DOI10.1093/imrn/rnv195zbMath1404.60009arXiv1501.04475OpenAlexW2105321865MaRDI QIDQ4560417

Francesco Mezzadri, Tom Claeys, Max R. Atkin

Publication date: 12 December 2018

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04475

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 (14)

Singular values for products of two coupled random matrices: hard edge phase transition ⋮ Critical edge behavior in the singularly perturbed Pollaczek–Jacobi type unitary ensemble ⋮ Hankel determinants for a Gaussian weight with Fisher–Hartwig singularities and generalized Painlevé IV equation ⋮ Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system ⋮ Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system ⋮ Gap Probability at the Hard Edge for Random Matrix Ensembles with Pole Singularities in the Potential ⋮ On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble ⋮ Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight ⋮ Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ Perturbed Hankel determinant, correlation functions and Painlevé equations ⋮ Moments of random matrices and hypergeometric orthogonal polynomials ⋮ Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation

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