Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics

Abstract

In this short note, we build upon some recent results to present a precise expression for the asymptotic variance of the Euler-Poincaré characteristic for the excursion sets of Gaussian eigenfunctions on ${\mathcal{S}}^2$.

References in corpus (2)

• A Gaussian kinematic formula
• Excursion probability of Gaussian random fields on sphere

Cited by in corpus (6)

• Nodal Lengths in Shrinking Domains for Random Eigenfunctions on ${\mathbb{S}}^2$
• Gaussian Random Measures Generated by Berry's Nodal Sets
• Fluctuations of the number of excursion sets of planar Gaussian fields
• The Defect of Random Hyperspherical Harmonics
• Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields
• Three central limit theorems for the unbounded excursion component of a Gaussian field