On 3-dimensional Berry's model

2019/12/20 by Federico Dalmao, Dalmao, Federico, Anne Estrade +3 · 4 citations
Earth and Planetary Sciences · Mathematics · #FOS: Mathematics #Geology and Paleoclimatology Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1912.09774

openalex publication_date 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work aims to study the dislocation or nodal lines of 3D Berry's random wave model. Their expected length is computed both in the isotropic and anisotropic cases, being them compared. Afterwards, in the isotropic case the asymptotic variance and distribution of the length are obtained as the domain grows to the whole space. Under some integrability condition on the covariance function, a central limit theorem is established. The study includes the Berry's monochromatic random waves, the Bargmann-Fock model and the Black-Body radiation as well as a power law model that exhibits an unusual asymptotic behaviour and yields a non-central limit theorem.

Cited by

• Universal Cancellations in Uniform Random Waves
• Gaussian random field's anisotropy using excursion sets
• Level area of spin random fields: a chaos decomposition
• New chaos decomposition of Gaussian nodal volumes

Related

• Fluctuations of the Nodal Number in the Two-Energy Planar Berry Random Wave Model
• A note on 3d-monochromatic random waves and cancellation
• On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
• Small Scale CLTs for the Nodal Length of Monochromatic Waves
• A relation between two different formulations of the Berry's conjecture