Fluctuations in the number of nodal domains
arXiv:2006.07730 · doi:10.1063/5.0018588
Abstract
We show that the variance of the number of connected components of the zero set of the two-dimensional Gaussian ensemble of random spherical harmonics of degree n grows as a positive power of n. The proof uses no special properties of spherical harmonics and works for any sufficiently regular ensemble of Gaussian random functions on the two-dimensional sphere with distribution invariant with respect to isometries of the sphere. Our argument connects the fluctuations in the number of nodal lines with those in a random loop ensemble on planar graphs of degree four, which can be viewed as a step towards justification of the Bogomolny-Schmit heuristics.
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Cited by in corpus (4)
- Fluctuations of the number of excursion sets of planar Gaussian fields
- Universality of nodal count distribution in large metric graphs
- A central limit theorem for the number of excursion set components of Gaussian fields
- A covariance formula for the number of excursion set components of Gaussian fields and applications