Random Complex Zeroes and Random Nodal Lines

TL;DR

This paper reviews recent advances in understanding the zero sets of Gaussian random functions, focusing on Gaussian entire functions with invariant zero distributions and Gaussian spherical harmonics on the sphere.

Contribution

It summarizes recent progress in analyzing the geometric properties of zero sets of specific Gaussian random functions.

Findings

Zero sets exhibit invariant distributions under isometries.

Progress in understanding nodal lines of Gaussian spherical harmonics.

Insights into the geometric structure of random zero sets.

Abstract

In these notes, we describe the recent progress in understanding the zero sets of two remarkable Gaussian random functions: the Gaussian entire function with invariant distribution of zeroes with respect to isometries of the complex plane, and Gaussian spherical harmonics on the two-dimensional sphere.