We study asymptotic distribution of zeros of random holomorphic sections of
high powers of positive line bundles defined over projective homogenous
manifolds. We work with a wide class of distributions that includes real and
complex Gaussians. As a special case, we obtain asymptotic zero distribution of
multivariate complex polynomials given by linear combinations of orthogonal
polynomials with i.i.d. random coefficients. Namely, we prove that normalized
zero measures of m i.i.d random polynomials, orthonormalized on a regular
compact set KβCm, are almost surely asymptotic to the
equilibrium measure of K.Comment: Final version incorporates referee comments. To appear in Indiana
Univ. Math.