Nodal intersections for random waves on the 3-dimensional torus

Zeev Rudnick, Igor Wigman, Nadav Yesha

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)
171 Downloads (Pure)

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- INSTITUT FOURIER
Volume66
Issue number6
DOIs
Publication statusPublished - 2016

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