Hole probabilities of random zeros on compact Riemann surfaces

TL;DR

This paper provides an estimate for how quickly the probability of finding no zeros (holes) in a region decreases for random holomorphic sections on compact Riemann surfaces.

Contribution

It introduces a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.

Findings

Derived a quantitative estimate for hole probability convergence.

Applicable to various compact Riemann surfaces.

Enhances understanding of zero distribution in random holomorphic sections.

Abstract

We establish a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.