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On the number of nodal domains of random spherical harmonics
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 5, October 2009
- pp. 1337-1357
- 10.1353/ajm.0.0070
- Article
- Additional Information
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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.