Functional Convergence of Berry's Nodal Lengths
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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