Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations

Name: Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations
Creator: Van Assche, Walter
Keywords: Mathematics - Classical Analysis and ODEs, 4. Education, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C45, 42C05, 60B20, 33E17, 0101 mathematics, 16. Peace & justice, 01 natural sciences

Van Assche, Walter

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http://arxiv.org/pdf...arrow_drop_down

http://arxiv.org/pdf/1904.0751...

Part of book or chapter of book

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arXiv.org e-Print Archive

Preprint . 2019

Data sources: arXiv.org e-Print Archive

https://doi.org/10.1007/978-3-...

Part of book or chapter of book . 2020 . Peer-reviewed

License: Springer TDM

Data sources: Crossref

https://dx.doi.org/10.48550/ar...

Article . 2019

License: arXiv Non-Exclusive Distribution

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https://dx.doi.org/10.1007/978...

Other literature type

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Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint , Other literature type 01 Jan 2020Embargo end date: 01 Jan 2019 English Publisher:Springer International Publishing

Authors: Van Assche, Walter;

doi: 10.1007/978-3-030-36744-2_22 , 10.48550/arxiv.1904.07518

arXiv: 1904.07518

Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations

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Abstract

Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics and probability and many other disciplines. In these notes we give an introduction to the use of orthogonal polynomials in random matrix theory, we explain the notion of multiple orthogonal polynomials, and we show the link with certain non-linear difference and differential equations known as Painlev�� equations.

48 pages, 2 figures

Related Organizations

KU Leuven
Belgium
Katholieke Universiteit Leuven
Belgium

Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C45, 42C05, 60B20, 33E17

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