On April 6th, the seminar series welcomed Prof. Anna Vidotto from the University of Naples Federico II to present recent work completed with Domenico Marinucci and Maurizia Rossi.
Title
On the excursion area of time dependent spherical random fields
Abstract
In this paper, we consider isotropic and stationary real Gaussian random fields defined on S2×R and we investigate the asymptotic behavior, as T→+∞, of the empirical measure (excursion area) in S2×[0,T] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and non-integrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry’s cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.