Empirical measure distribution of random fields on the sphere evolving over time.

D. Marinucci, M. Rossi, A. Vidotto

We consider isotropic and stationary real Gaussian random fields defined on sphere-cross-time and we investigate the asymptotic behavior, for large time, of the average empirical process 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. (Based on a joint work with Domenico Marinucci and Anna Vidotto.)

Keywords: Time dependent spherical random fields, excursion area, limit theorems, Wiener chaos.

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HC2: Canónigos Room 2

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