Pavel Bleher, Bernard Shiffman, Steve Zelditch 
Universality and scaling of correlations between zeros on complex manifolds
(144K, Latex2e, 3 eps figures)

ABSTRACT.  We study the limit as $N\to\infty$ of the correlations between 
simultaneous zeros of random sections of the powers $L^N$ of a positive 
holomorphic line bundle $L$ over a compact complex manifold $M$, when 
distances are rescaled so that the average density of zeros is 
independent of $N$. We show that the limit correlation is independent of 
the line bundle and depends only on the dimension of $M$ and the 
codimension of the zero sets. We also provide some explicit formulas for 
pair correlations. In particular, we provide an alternate derivation of 
Hannay's limit pair correlation function for SU(2) polynomials, and we 
show that this correlation function holds for all compact Riemann 
surfaces.