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

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).

38 pages, 1 figure

References in corpus (1)

• Gaussian processes, kinematic formulae and Poincaré's limit

Cited by in corpus (1)

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