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Todino, Anna Paola

Limiting behavior for the excursion area of band-limited spherical random fields. (English) Zbl 1522.60047

Electron. Commun. Probab. 27, 1-12 (2022).
Summary: In this paper we investigate some geometric functionals for band-limited Gaussian and isotropic spherical random fields in dimension 2. In particular, we focus on the area of excursion sets, providing its behavior in the high energy limit. Our results are based on Wiener chaos expansion for non linear transform of Gaussian fields and on an explicit derivation on the high-frequency limit of the covariance function of the field. As a simple corollary we establish also the Central Limit Theorem for the excursion area.

Cited in 1 Document

MSC:

60G60 Random fields
33C55 Spherical harmonics
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
60F05 Central limit and other weak theorems

Keywords:

central limit theorem; excursion area; Gaussian eigenfunctions; Hilb’s asymptotics; Wiener-chaos expansion
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References:

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