Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight

DOI10.1016/j.jat.2014.12.003zbMath1314.33021arXiv1407.7334OpenAlexW2091470872MaRDI QIDQ2256604

Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao

Publication date: 20 February 2015

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.7334

zbMATH Keywords

asymptoticsRiemann-Hilbert problemHankel determinantPainlevé III equationLaguerre weight

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Painlevé-type functions (33E17)

Related Items (16)

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 ⋮ Asymptotic relations for semi-classical Laguerre orthogonal polynomials and the associated Hankel determinants ⋮ Painlevé III Asymptotics of Hankel Determinants for a Perturbed Jacobi Weight ⋮ On a distinguished family of random variables and Painlevé equations ⋮ The smallest eigenvalue of the ill-conditioned Hankel matrices associated with a semi-classical Hermite weight ⋮ Critical edge behavior in the singularly perturbed Pollaczek–Jacobi type unitary ensemble ⋮ Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble ⋮ Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: From finite n to large n asymptotics ⋮ A singular linear statistic for a perturbed LUE and the Hankel matrices ⋮ Gap Probability at the Hard Edge for Random Matrix Ensembles with Pole Singularities in the Potential ⋮ 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 ⋮ Semi-classical Jacobi polynomials, Hankel determinants and asymptotics ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation ⋮ Hankel determinants for a singular complex weight and the first and third Painlevé transcendents

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