On the correlation between nodal and boundary lengths for random spherical harmonics

Marinucci, Domenico; Rossi, Maurizia

doi:10.48550/arxiv.1902.05750

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Cited by 2 publications

(2 citation statements)

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“…Such functional is the so-called (centered) sample power spectrum, which is defined as the integral of H 2 (f k ), where H 2 is the second Hermite polynomial. Moreover, in [MR19], it was proved that the correlation between…”

Section: Motivationmentioning

confidence: 99%

A Note on the Reduction Principle for the Nodal Length of Planar Random Waves

Vidotto¹

2020

Preprint

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Inspired by the recent work [MRW20], we prove that the nodal length of a planar random wave B E , i.e. the length of its zero set B −1 E (0), is asymptotically equivalent, in the L 2 -sense and in the high-frequency limit E → ∞, to the integral of H 4 (B E (x)), H 4 being the fourth Hermite polynomial. As a straightforward consequence, we obtain a central limit theorem in Wasserstein distance. This complements recent findings in [NPR19] and [PV20].

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Section: Motivationmentioning

confidence: 99%

A Note on the Reduction Principle for the Nodal Length of Planar Random Waves

Vidotto¹

2020

Preprint

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“…Canzani and Hanin [9] studied the universality phenomenon in general Riemannian manifolds. The reader can find results on arithmetic random waves defined on the flat torus [7,10] and on random spherical harmonics in [8,15,18] and references therein, see also [23] for a survey on both subjects. The nodal sets of Berry's planar random waves, i.e.…”

Section: Introductionmentioning

confidence: 99%

On 3-dimensional Berry's model

Dalmao¹,

Estrade²,

León³

2019

Preprint

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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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On the correlation between nodal and boundary lengths for random spherical harmonics

Cited by 2 publications

References 22 publications

A Note on the Reduction Principle for the Nodal Length of Planar Random Waves

A Note on the Reduction Principle for the Nodal Length of Planar Random Waves

On 3-dimensional Berry's model

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