A reduction principle for the critical values of random spherical harmonics

Valentina Cammarota and Domenico Marinucci

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 2433-2470

Abstract: We study here the random fluctuations in the number of critical points with values in an interval I⊂R for Gaussian spherical eigenfunctions fℓ, in the high energy regime where ℓ→∞. We show that these fluctuations are asymptotically equivalent to the centred L2-norm of fℓ times the integral of a (simple and fully explicit) function over the interval under consideration. We discuss also the relationships between these results and the asymptotic behaviour of other geometric functionals on the excursion sets of random spherical harmonics.

Keywords: Reduction principle; Critical points; Wiener-Chaos expansion; Spherical harmonics; Quantitative central limit theorem; Berry’s cancellation phenomenon (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2019.07.006

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