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**Harvard**

Berman, R. (2009) *Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n*.

** BibTeX **

@article{

Berman2009,

author={Berman, Robert},

title={Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n},

journal={Indiana University Mathematics Journal},

issn={0022-2518},

volume={58},

issue={4},

pages={1921-1946},

abstract={Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is differentiable and all of its first partial derivatives are locally Lipshitz continuous. The convergence is studied in the large k limit and is expressed in terms of the global equilibrium potential associated to the weight function, as well as in terms of the Monge-Ampere measure of the weight function itself on a certain set. A setting of polynomials associated to a given Newton polytope, scaled by k, is also considered. These results apply directly to the study of the distribution of zeroes of random polynomials and of the eigenvalues of random normal matrices. },

year={2009},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 113195

A1 Berman, Robert

T1 Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

YR 2009

JF Indiana University Mathematics Journal

SN 0022-2518

VO 58

IS 4

SP 1921

OP 1946

AB Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is differentiable and all of its first partial derivatives are locally Lipshitz continuous. The convergence is studied in the large k limit and is expressed in terms of the global equilibrium potential associated to the weight function, as well as in terms of the Monge-Ampere measure of the weight function itself on a certain set. A setting of polynomials associated to a given Newton polytope, scaled by k, is also considered. These results apply directly to the study of the distribution of zeroes of random polynomials and of the eigenvalues of random normal matrices.

LA eng

DO 10.1512/iumj.2009.58.3644

LK http://dx.doi.org/10.1512/iumj.2009.58.3644

OL 30