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.