On the Number of Nodal Domains of Random Spherical Harmonics

  • Published 2008
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 tends to a positive constant a, and that N(f)/n exponentially concentrates around a. This result is consistent with predictions made by Bogomolny and Schmit using a percolation-like model for nodal domains of… CONTINUE READING