We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval I ⊂ ℝ. We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random L2-norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics.

Cammarota, V., Todino, A. (2022). On the correlation between critical points and critical values for random spherical harmonics. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 106, 41-62 [10.1090/tpms/1164].

On the correlation between critical points and critical values for random spherical harmonics

Todino, A. P.
2022

Abstract

We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval I ⊂ ℝ. We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random L2-norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics.
Articolo in rivista - Articolo scientifico
Critical points; Partial correlation; Spherical harmonics; Wiener-Chaos expansion;
English
41
62
22
Cammarota, V., Todino, A. (2022). On the correlation between critical points and critical values for random spherical harmonics. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 106, 41-62 [10.1090/tpms/1164].
Cammarota, V; Todino, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/376760
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