Fluctuations of Level Curves for Time-Dependent Spherical Random Fields

The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this paper, we extend this framework by considering fluctuations over time for the level curves of general isotropic Gaussian spherical random fields. We focus on both long and short memory assumptions; in the former case, we show that the fluctuations of u-level curves are dominated by a single component, corresponding to a second-order chaos evaluated on a subset of the multipole components for the random field.