Points on nodal lines with given direction

Zeév Rudnick, Igor Wigman

Research output: Contribution to journalArticlepeer-review


We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

Original languageEnglish
Pages (from-to)927-953
Number of pages27
JournalJournal of Spectral Theory
Issue number3
StatePublished - 2020


  • Arithmetic random waves
  • Gradient direction
  • Nodal line
  • Toral laplace eigenfunctions
  • Zero set

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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