Equidistribution of zeros of random holomorphic sections

By Turgay Bayraktar. 2013

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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 $K\subset \Bbb{C}^m,$ are almost surely asymptotic to the equilibrium measure of $K$.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1ba274b4199c6e78bf72525d3e96bb160ec3b4ab