Poincaré–Lelong Approach to Universality and Scaling of Correlations Between Zeros
- Cite this article as:
- Bleher, P., Shiffman, B. & Zelditch, S. Comm Math Phys (2000) 208: 771. doi:10.1007/s002200050010
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This note is concerned with the scaling limit as N→∞ 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 LN of any positive holomorphic line bundle L over a compact Kähler 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.