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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2021

On 3-dimensional Berry's model

Résumé

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.
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Dates et versions

hal-02478307 , version 1 (13-02-2020)

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Federico Dalmao, Anne Estrade, José Rafael León. On 3-dimensional Berry's model. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18, pp.379-399. ⟨10.30757/ALEA.v18-17⟩. ⟨hal-02478307⟩
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