On the number of nodal domains of random spherical harmonics

Fedor Nazarov, Mikhail Sodin

Research output: Contribution to journalArticlepeer-review

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 a, and that N(f)/n 2 exponentially concentrates around a. This result is consistent with predictions made by Bogomolny and Schmit using a percolation-like model for nodal domains of random Gaussian plane waves.

Original languageEnglish
Pages (from-to)1337-1357
Number of pages21
JournalAmerican Journal of Mathematics
Volume131
Issue number5
DOIs
StatePublished - 2009

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