Geodesic
Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials
Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 600-620

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DOI

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.
DOI : 10.4153/CJM-2012-016-x
Mots-clés : 42C05, 42C99, 42B05, 60B20, orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functions 
Kroó, A.; Lubinsky, D. S. Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials. Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 600-620. doi: 10.4153/CJM-2012-016-x
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     title = {Christoffel {Functions} and {Universality} in the {Bulk} for {Multivariate} {Orthogonal} {Polynomials}},
     journal = {Canadian journal of mathematics},
     pages = {600--620},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-016-x/}
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