Poincare-Lelong approach to universality and scaling of correlations between zeros

Details Poincare-Lelong approach to universality and scaling of correlations between zeros Poincare-Lelong approach to universality and scaling of correlations between zeros

1999-03-05

arxiv.org/abs/math-ph/9903012v1

Commun. Math. Phys. 208 (2000), 771-785.

Physics

Mathematical Physics

Scientific paper

10.1007/s002200050010

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.

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