On the Number of Nodal Domains of Random Spherical Harmonics

Abstract

Let N(f) be a number of nodal domains of a random Gaussian spherical harmonic f of degree n. We prove that as n grows to infinity, the mean of N(f)/n^2 tends to a positive constant, and that N(f)/n^2 exponentially concentrates around that constant. This result is consistent with predictions made by Bogomolny and Schmit using a percolation-like model for nodal domains of random Gaussian plane waves.

20 pages

References in corpus (2)

• Nodal domains statistics - a criterion for quantum chaos
• Percolation model for nodal domains of chaotic wave functions

Cited by in corpus (5)

• Random wave functions and percolation
• Local and global analysis of eigenfunctions
• Nodal domains on graphs - How to count them and why?
• On spectral minimal partitions: the case of the sphere
• Counting open nodal lines of random waves on planar domains