Nodal intersections for random waves on the 3-dimensional torus

Zeév Rudnick, Igor Wigman, Nadav Yesha

Research output: Contribution to journalArticlepeer-review


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
Issue number6
StatePublished - 2016
Externally publishedYes

Bibliographical note

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


  • 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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