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

2021/07/31 by Valentina Cammarota, Cammarota, Valentina, Anna Paola Todino +1
Mathematics · #33C55 #42C10 #60D05 #60G60 #62M15 #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2108.00229

openalex publication_date 2021/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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