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arXiv · 1510.00339

Fluctuations of the total number of critical points of random spherical harmonics

Valentina Cammarota·Igor Wigman
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Abstract

We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate percolation process for modelling nodal domains of eigenfunctions on generic compact surfaces or billiards.

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Valentina Cammarota, Igor Wigman. 2015-10-01. Fluctuations of the total number of critical points of random spherical harmonics. https://doi.org/10.1016/j.spa.2017.02.013

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