We consider polynomial transforms (polyspectra) of Berry’s model – the Euclidean Random Wave model – and of Random Hyperspherical Harmonics. We determine the asymptotic behavior of variance for polyspectra of any order in the high-frequency limit. In particular, we are able to treat polyspectra of any odd order q ≥ 5, whose asymptotic behavior was left as a conjecture in the case of Random Hyperspherical Harmonics by Marinucci and Wigman (Comm. Math. Phys. 2014). To this end, we exploit a relation between the variance of polyspectra and the distribution of uniform random walks on Euclidean space with finitely many steps, which allows us to rely on technical results in the latter context.

Grotto, F., Maini, L., Todino, A. (2024). Fluctuations of polyspectra in spherical and Euclidean random wave models. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 29 [10.1214/24-ECP578].

Fluctuations of polyspectra in spherical and Euclidean random wave models

Maini, L;
2024

Abstract

We consider polynomial transforms (polyspectra) of Berry’s model – the Euclidean Random Wave model – and of Random Hyperspherical Harmonics. We determine the asymptotic behavior of variance for polyspectra of any order in the high-frequency limit. In particular, we are able to treat polyspectra of any odd order q ≥ 5, whose asymptotic behavior was left as a conjecture in the case of Random Hyperspherical Harmonics by Marinucci and Wigman (Comm. Math. Phys. 2014). To this end, we exploit a relation between the variance of polyspectra and the distribution of uniform random walks on Euclidean space with finitely many steps, which allows us to rely on technical results in the latter context.
Articolo in rivista - Articolo scientifico
Bessel functions; Gaussian eigenfunctions; random walk;
English
4-mar-2024
2024
29
9
none
Grotto, F., Maini, L., Todino, A. (2024). Fluctuations of polyspectra in spherical and Euclidean random wave models. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 29 [10.1214/24-ECP578].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/481599
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