1. CJM 2012 (vol 65 pp. 600)
|Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials|
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:orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functions
Categories:42C05, 42C99, 42B05, 60B20