Non-universal fluctuations of the empirical measure for sphere-cross-time random fields
In this talk we consider isotropic and stationary real Gaussian sphere-cross-time random fields and we investigate the large time asymptotic behavior of the empirical measure at any threshold, covering both cases when the field exhibits short and long memory, i.e 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. (This talk is based on a joint work with D. Marinucci and A. Vidotto)