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Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

A. Kroó  and
D. S. Lubinsky
A. Kroó
Affiliation:
Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u.13-15, Budapest H-1053, Hungary, e-mail: kroo@renyi.hu
D. S. Lubinsky
Affiliation:
Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u.13-15, Budapest H-1053, Hungary, e-mail: kroo@renyi.hu
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Abstract

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We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain. In particular, this is true if they are positive a.e. on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex under far more general conditions than previously known. As another consequence, we establish universality type limits in the bulk in a variety of settings.

Keywords

42C0542C9942B0560B20orthogonal polynomialsrandom matricesunitary ensemblescorrelation functionsChristoffel functions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 3 , 01 June 2013 , pp. 600 - 620
Copyright
Copyright © Canadian Mathematical Society 2013

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