Nodal intersections for random waves on the 3-dimensional torus

Zeév Rudnick, Igor Wigman, Nadav Yesha

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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 languageEnglish
Pages (from-to)2455-2484
Number of pages30
JournalAnnales de l'Institut Fourier
Volume66
Issue number6
DOIs
StatePublished - 2016

Funding

FundersFunder number
European Commission
Seventh Framework Programme335141, 320755

    Keywords

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

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