TY - JOUR

T1 - Poincaré-Lelong approach to universality and scaling of correlations between zeros

AU - Bleher, Pavel

AU - Shiffman, Bernard

AU - Zelditch, Steve

PY - 2000/1

Y1 - 2000/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s002200050010

DO - 10.1007/s002200050010

M3 - Article

AN - SCOPUS:0034349882

VL - 208

SP - 771

EP - 785

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -