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

Research output: Contribution to journalArticle

Original languageEnglish
JournalStochastic Processes and Their Applications
Early online date23 Mar 2017
DOIs
Accepted/In press23 Mar 2017
E-pub ahead of print23 Mar 2017

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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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