We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry’s random wave model to a finite collection of (possibly overlapping) smooth compact subsets of R2. Our main result shows that, as the energy diverges to infinity and after an adequate normalisation, these random elements converge in distribution to a Gaussian vector, whose covariance structure reproduces that of a homogeneous independently scattered random measure. A by-product of our analysis is that, when restricted to rectangles, the dominant chaotic projection of the nodal length field weakly converges to a standard Wiener sheet, in the Banach space of real-valued continuous mappings over a fixed compact set. An analogous study is performed for complex-valued random waves, in which case the nodal set is a locally finite collection of random points.
Gaussian Random Measures Generated by Berry’s Nodal Sets / Peccati, G.; Vidotto, A.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 178:4(2020), pp. 996-1027. [10.1007/s10955-019-02477-z]
Gaussian Random Measures Generated by Berry’s Nodal Sets
Vidotto A.
2020
Abstract
We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry’s random wave model to a finite collection of (possibly overlapping) smooth compact subsets of R2. Our main result shows that, as the energy diverges to infinity and after an adequate normalisation, these random elements converge in distribution to a Gaussian vector, whose covariance structure reproduces that of a homogeneous independently scattered random measure. A by-product of our analysis is that, when restricted to rectangles, the dominant chaotic projection of the nodal length field weakly converges to a standard Wiener sheet, in the Banach space of real-valued continuous mappings over a fixed compact set. An analogous study is performed for complex-valued random waves, in which case the nodal set is a locally finite collection of random points.File | Dimensione | Formato | |
---|---|---|---|
Peccati,Vidotto2020.pdf
accesso aperto
Tipologia:
Versione Editoriale (PDF)
Licenza:
Dominio pubblico
Dimensione
523.09 kB
Formato
Adobe PDF
|
523.09 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.