On the Number of Nodal Domains of Random Spherical Harmonics

Fedor Nazarov; Mikhail Sodin

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arXiv · 0706.2409

On the Number of Nodal Domains of Random Spherical Harmonics

Fedor Nazarov·Mikhail Sodin

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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.

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Fedor Nazarov, Mikhail Sodin. 2007-06-18. On the Number of Nodal Domains of Random Spherical Harmonics. https://arxiv.org/abs/0706.2409

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