Points on nodal lines with given direction
Spectral Theory
2018-07-31 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1802.09603,
title = {Points on nodal lines with given direction},
author = {Zeev Rudnick and Igor Wigman},
journal= {arXiv preprint arXiv:1802.09603},
year = {2018}
}
Comments
The statement and the proof of Theorem 1.2 corrected