Bergman kernels for weighted polynomials and weighted equilibrium measures of $\mathbb{C}^{n}$ Robert Berman 32A2532L1032U1542C05Bergman kernel asymptoticsglobal pluripotential theoryorthogonal polynomials Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in $\mathbb{C}^{n}$ of total degree at most $k$, equipped with a weighted norm, are obtained. The weight function $\phi$ is assumed to be $\mathcal{C}^{1,1}$, i.e. $\phi$ is differentiable and all of its first partial derivatives are locally Lipschitz 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-Amp\'ere measure of the weight function itself on a certain set. These results apply directly to the study of the distribution of zeroes of random polynomials and of the eigenvalues of random normal matrices. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3644 10.1512/iumj.2009.58.3644 en Indiana Univ. Math. J. 58 (2009) 1921 - 1946 state-of-the-art mathematics http://iumj.org/access/