On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics

Valentina Cammarota () and Domenico Marinucci ()
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Valentina Cammarota: Sapienza University of Rome
Domenico Marinucci: University of Rome Tor Vergata

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2269-2303

Abstract: Abstract We prove a Central Limit Theorem for the critical points of random spherical harmonics, in the high-energy limit. The result is a consequence of a deeper characterization of the total number of critical points, which are shown to be asymptotically fully correlated with the sample trispectrum, i.e. the integral of the fourth Hermite polynomial evaluated on the eigenfunctions themselves. As a consequence, the total number of critical points and the nodal length are fully correlated for random spherical harmonics, in the high-energy limit.

Keywords: Random fields; Critical points; Wiener chaos expansion; Spherical harmonics; Berry’s cancellation phenomenon; 60G60; 62M15; 53C65; 42C10; 33C55 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01136-y

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