Nodal intersections for random waves on the 3-dimensional torus

Zeév Rudnick; Igor Wigman; Nadav Yesha

doi:10.5802/aif.3068

Nodal intersections for random waves on the 3-dimensional torus

Zeév Rudnick, Igor Wigman, Nadav Yesha

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard three-dimensional flat torus with a fixed smooth reference curve, which has nowhere vanishing curvature. The expected intersection number is universally proportional to the length of the reference curve, times the wavenumber, independent of the geometry. Our main result gives a bound for the variance, if either the torsion of the curve is nowhere zero or if the curve is planar.

Original language	English
Pages (from-to)	2455-2484
Number of pages	30
Journal	Annales de l'Institut Fourier
Volume	66
Issue number	6
DOIs	https://doi.org/10.5802/aif.3068
State	Published - 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Association des Annales de l'institut Fourier, 2016.

Keywords

Asymptotics
Curvature
Intersection points
Laplace eigenfunctions
Nodal line
Test curve
Torus
Variance

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.3068

Cite this

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AB - We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard three-dimensional flat torus with a fixed smooth reference curve, which has nowhere vanishing curvature. The expected intersection number is universally proportional to the length of the reference curve, times the wavenumber, independent of the geometry. Our main result gives a bound for the variance, if either the torsion of the curve is nowhere zero or if the curve is planar.

KW - Asymptotics

KW - Curvature

KW - Intersection points

KW - Laplace eigenfunctions

KW - Nodal line

KW - Test curve

KW - Torus

KW - Variance

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Nodal intersections for random waves on the 3-dimensional torus

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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