In recent years, considerable interest has been drawn by the analysis of geometric functionals for the excursion sets of random eigenfunctions on the unit sphere (spherical harmonics). In this paper, we extend those results to proper subsets of the sphere S2, i.e., spherical caps, focussing, in particular, on the excursion area. Precisely, we show that the asymptotic behaviour of the excursion area is dominated by the so-called second-order chaos component and we exploit this result to establish a quantitative central limit theorem, in the high energy limit. These results generalize analogous findings for the full sphere; their proofs, however, require more sophisticated techniques, in particular, a careful analysis (of some independent interest) for smooth approximations of the indicator function for spherical cap subsets.

Todino, A. (2019). A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2. JOURNAL OF MATHEMATICAL PHYSICS, 60(2) [10.1063/1.5048976].

A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2

Todino, AP
2019

Abstract

In recent years, considerable interest has been drawn by the analysis of geometric functionals for the excursion sets of random eigenfunctions on the unit sphere (spherical harmonics). In this paper, we extend those results to proper subsets of the sphere S2, i.e., spherical caps, focussing, in particular, on the excursion area. Precisely, we show that the asymptotic behaviour of the excursion area is dominated by the so-called second-order chaos component and we exploit this result to establish a quantitative central limit theorem, in the high energy limit. These results generalize analogous findings for the full sphere; their proofs, however, require more sophisticated techniques, in particular, a careful analysis (of some independent interest) for smooth approximations of the indicator function for spherical cap subsets.
Articolo in rivista - Articolo scientifico
Gaussian Eigenfunctions; Spherical Harmonics; Excursion Area; Quantitative Central Limit Theorem; Wiener-chaos expansion; Clebsch-Gordan coefficients;
English
Todino, A. (2019). A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2. JOURNAL OF MATHEMATICAL PHYSICS, 60(2) [10.1063/1.5048976].
Todino, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/374825
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