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arXiv · 2208.07580

Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder

Massimo Notarnicola·Giovanni Peccati·Anna Vidotto
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Abstract

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. Our analysis is 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. Such an exact characterization is then combined with moment estimates for suprema of stationary Gaussian random fields, and with a tightness criterion by Davydov and Zikitis (2005).

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Massimo Notarnicola, Giovanni Peccati, Anna Vidotto. 2022-08-16. Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder. https://doi.org/10.1007/s10955-023-03111-9

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