Random zeros on complex manifolds and Bergman kernel asymptotics
Independent random points on a compact Riemann surface tend to cluster, while the zeros of a random holomorphic section of a line bundle of high degree tend to repel on account of their correlations. I shall dis-cuss asymptotic formulas for the distribution and pair correlation of zeros of Gaussian random polynomials on C^n and, more generally, of random sections of powers of a positive line bundle on a compact Kahler manifold. These formulas depend on the off-diagonal asymptotic expansion of the Bergman kernel, which also yields central limit theorems for the zeros.
