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Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials |
Canad. J. Math. 65(2013), 600-620
Published:2012-08-25
Printed: Jun 2013
Printed: Jun 2013
- A. Kroó,
- D. S. Lubinsky,
Abstract
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 |
| MSC Classifications: |
42C05 - Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45] 42C99 - None of the above, but in this section 42B05 - Fourier series and coefficients 60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52) |