Limiting Behavior for the Excursion Area of Band-Limited Spherical Random Fields

DOI10.1214/22-ECP488arXiv2003.01634MaRDI QIDQ6336062

Publication date: 3 March 2020

Abstract: 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 result is 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.

Mathematics Subject Classification ID

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

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