On the universality of the Nazarov-Sodin constant

TL;DR

This paper investigates the number of connected components of non-Gaussian random spherical harmonics on the sphere, showing that the expected count is universal across distributions with finite second moments.

Contribution

It proves the universality of the expected number of nodal domains for non-Gaussian spherical harmonics, extending previous Gaussian results.

Findings

Expected nodal domains count is distribution-independent

Universality holds for distributions with finite second moments

Results apply to non-Gaussian random spherical harmonics

Abstract

We study the number of connected components of non-Gaussian random spherical harmonics on the two dimensional sphere $\mathbb{S}^2$. We prove that the expectation of the nodal domains count is independent of the distribution of the coefficients provided it has a finite second moment.