Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder
arXiv:2208.07580 · doi:10.1007/s10955-023-03111-9
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).
arXiv comment38 pages, 1 figure
References in corpus (9)
- Hyperuniform States of Matter
- Fluctuations of the nodal length of random spherical harmonics, erratum
- On the Excursion Sets of Spherical Gaussian Eigenfunctions
- Phase Singularities in Complex Arithmetic Random Waves
- Gaussian Random Measures Generated by Berry's Nodal Sets
- Nodal Statistics of Planar Random Waves
- Gaussian processes, kinematic formulae and Poincaré's limit
- Local Weak Limits of Laplace Eigenfunctions
- Fluctuations of the increment of the argument for the Gaussian entire function