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

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.

References in corpus (3)

• Joint Planck and WMAP CMB Map Reconstruction
• Subsampling needlet coefficients on the sphere
• On the distribution of the critical values of random spherical harmonics

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