Orthogonal and multiple orthogonal polynomials, random matrices, and Painlev\'e equations
Classical Analysis and ODEs
2020-07-14 v2
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\'e equations.
Keywords
Cite
@article{arxiv.1904.07518,
title = {Orthogonal and multiple orthogonal polynomials, random matrices, and Painlev\'e equations},
author = {Walter Van Assche},
journal= {arXiv preprint arXiv:1904.07518},
year = {2020}
}
Comments
48 pages, 2 figures