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Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials

  Published:2012-08-25
 Printed: Jun 2013
  • A. Kroó,
    Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u.13-15, Budapest H-1053, Hungary
  • D. S. Lubinsky,
    School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
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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 orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functions
MSC Classifications: 42C05, 42C99, 42B05, 60B20 show english descriptions Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
None of the above, but in this section
Fourier series and coefficients
Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
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)
 

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