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

V. Cammarota and I. Wigman

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 3825-3869

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.

Keywords: Spherical harmonics; Critical points; Kac-Rice formula; Legendre polynomials; Hilb’s asymptotics (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:12:p:3825-3869

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DOI: 10.1016/j.spa.2017.02.013

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