Functional Convergence of Berry's Nodal Lengths

Vidotto Anna, Università degli Studi di Napoli Federico II

In this talk, we consider Berry’s random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. We will see that our results are crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos, whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. The talk is based on a joint work with M. Notarnicola and G. Peccati.

Area: IS8 - Random Fields (Maurizia Rossi)

Keywords: Central Limit Theorems; Functional Convergence; Gaussian Fields; Nodal Sets; Random Waves; Total Disorder.

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