ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS

V. Cammarota; A. P. Todino

doi:10.1090/tpms/1164

ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

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.

Lingua originale	Inglese
pagine (da-a)	41-62
Numero di pagine	22
Rivista	Theory of Probability and Mathematical Statistics
Volume	106
DOI	https://doi.org/10.1090/tpms/1164
Stato di pubblicazione	Pubblicato - 2022
Pubblicato esternamente	Sì

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title = "ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS",

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.",

keywords = "Critical points, Partial correlation, Spherical harmonics, Wiener-Chaos expansion",

author = "V. Cammarota and Todino, {A. P.}",

note = "Publisher Copyright: {\textcopyright} 2022 Taras Shevchenko National University of Kyiv.",

year = "2022",

doi = "10.1090/tpms/1164",

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AU - Todino, A. P.

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Y1 - 2022

N2 - 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.

AB - 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.

KW - Critical points

KW - Partial correlation

KW - Spherical harmonics

KW - Wiener-Chaos expansion

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DO - 10.1090/tpms/1164

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JO - Theory of Probability and Mathematical Statistics

JF - Theory of Probability and Mathematical Statistics

ER -

ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS

Abstract

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