Equidistribution of Zeros of Random Holomorphic Sections for Moderate Measures

TL;DR

This paper proves that zeros of random holomorphic sections of high powers of line bundles become evenly distributed according to moderate measures, providing a convergence rate for this distribution.

Contribution

It introduces an equidistribution theorem for zeros of random sections with singular moderate measures and quantifies the convergence speed.

Findings

Zeros become equidistributed with respect to moderate measures

Provides explicit convergence speed for the distribution

Extends previous results to singular measures

Abstract

We establish an equidistribution theorem for the zeros of random holomorphic sections of high powers of a positive holomorphic line bundle. The equidistribution is associated with a family of singular moderate measures. We also give a convergence speed for the equidistribution.