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.
The author has been partially supported by “Progetto di Ricerca GNAMPA-INdAM”, codice CUP_E55F22000270001.
This topic was suggested by Domenico Marinucci and Igor Wigman. The author would like to thank them also for some useful discussions. Thanks also to an anonimous referee for some comments.
"Limiting behavior for the excursion area of band-limited spherical random fields." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP488