Large N-limit for random matrices with external source with three distinct eigenvalues

DOI10.1142/S2010326316500052zbMath1381.60023arXiv1510.00323MaRDI QIDQ2809330

Yang Chen, Jian Xu, En-gui Fan

Publication date: 27 May 2016

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

Full work available at URL: https://arxiv.org/abs/1510.00323

zbMATH Keywords

Riemann-Hilbert problemrandom matricesmultiple orthogonal polynomialslarge \(\mathrm{N}\)-limit

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Boundary value problems in the complex plane (30E25) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (2)

Long‐time asymptotics to the defocusing generalized nonlinear Schrödinger equation with the decaying initial value problem ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source

Cites Work

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• Multiple orthogonal polynomials
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• Correlations of nearby levels induced by a random potential
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Large \(n\) limit of Gaussian random matrices with external source. II
• Multiple orthogonal polynomials for classical weights

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