Asymptotic Normality of Divisors of Random Holomorphic Sections on Non-compact Complex Manifolds

TL;DR

This paper establishes a central limit theorem for the distribution of zero divisors of Gaussian holomorphic sections on non-compact complex manifolds, advancing understanding of their asymptotic behavior.

Contribution

It introduces a new CLT for linear statistics of zero divisors of Gaussian holomorphic sections on non-compact Hermitian manifolds.

Findings

Proves asymptotic normality of zero divisor statistics

Extends CLT results to non-compact complex manifolds

Provides a framework for analyzing zero distributions in complex geometry

Abstract

We prove a central limit theorem for smooth linear statistics related to the zero divisors of Gaussian i.i.d. centered holomorphic sections of tensor powers of a Hermitian holomorphic line bundle over a non-compact Hermitian manifold.