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.
ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS / Cammarota, Valentina; Paola Todino, Anna. - In: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS. - ISSN 0094-9000. - (2022), pp. 41-62.
ON THE CORRELATION BETWEEN CRITICAL POINTS AND CRITICAL VALUES FOR RANDOM SPHERICAL HARMONICS
Valentina Cammarota
Primo
;
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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Cammarota_correlations_2022.pdf.pdf
solo gestori archivio
Note: Cammarota_correlations_2022.pdf
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
321.97 kB
Formato
Adobe PDF
|
321.97 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
