The defect of toral Laplace eigenfunctions and Arithmetic Random Waves
Mathematical Physics
2021-09-01 v1 math.MP
Number Theory
Abstract
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic eigenfunctions averaged w.r.t. the spatial variable. In either scenario we exploit the associated symmetry of the eigenfunctions to show that the expectation (Gaussian or spatial) vanishes. Our principal results concern the high energy limit behaviour of the defect variance.
Cite
@article{arxiv.2006.11644,
title = {The defect of toral Laplace eigenfunctions and Arithmetic Random Waves},
author = {Par Kurlberg and Igor Wigman and Nadav Yesha},
journal= {arXiv preprint arXiv:2006.11644},
year = {2021}
}
Comments
27 pages, 1 figure