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.

Todino, A. (2022). Limiting behavior for the excursion area of band-limited spherical random fields. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 27, 1-12 [10.1214/22-ECP488].

Limiting behavior for the excursion area of band-limited spherical random fields

Todino, AP
2022

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 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.
Articolo in rivista - Articolo scientifico
Central Limit Theorem; Excursion Area; Gaussian Eigenfunctions; Hilb’s asymp-totics; Wiener-chaos expansion;
English
2022
27
1
12
open
Todino, A. (2022). Limiting behavior for the excursion area of band-limited spherical random fields. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 27, 1-12 [10.1214/22-ECP488].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/397922
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