Nodal intersections for random waves on the 3-dimensional torus
Number Theory
2016-05-13 v3 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.1501.07410,
title = {Nodal intersections for random waves on the 3-dimensional torus},
author = {Zeev Rudnick and Igor Wigman and Nadav Yesha},
journal= {arXiv preprint arXiv:1501.07410},
year = {2016}
}
Comments
26 pages. Some minor revision following referee's comments