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

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  • Cammarota, V.
  • Wigman, I.

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.

Suggested Citation

  • Cammarota, V. & Wigman, I., 2017. "Fluctuations of the total number of critical points of random spherical harmonics," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3825-3869.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:12:p:3825-3869
    DOI: 10.1016/j.spa.2017.02.013
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    Cited by:

    1. Valentina Cammarota & Domenico Marinucci, 2022. "On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2269-2303, December.
    2. Cammarota, Valentina & Marinucci, Domenico, 2020. "A reduction principle for the critical values of random spherical harmonics," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2433-2470.
    3. Muirhead, Stephen, 2020. "A second moment bound for critical points of planar Gaussian fields in shrinking height windows," Statistics & Probability Letters, Elsevier, vol. 160(C).

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