Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials

Kroó, A. ; Lubinsky, D. S.

Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 600-620

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-016-x

Mots-clés : 42C05, 42C99, 42B05, 60B20, orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functions

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