Pavel Bleher, Bernard Shiffman, Steve Zelditch
Poincare-Lelong approach to universality and scaling of
correlations between zeros
(41K, Latex 2e)
ABSTRACT. This note is concerned with the scaling limit as N approaches infinity
of n-point correlations between zeros of random holomorphic
polynomials of degree N in m variables. More generally we study
correlations between zeros of holomorphic sections of powers L^N of
any positive holomorphic line bundle L over a compact Kahler
manifold. Distances are rescaled so that the average density of zeros
is independent of N. Our main result is that the scaling limits of the
correlation functions and, more generally, of the "correlation forms"
are universal, i.e. independent of the bundle L, manifold M or point
on M.