Small scale equidistribution of random waves generated by an unfair coin flip
Analysis of PDEs
2021-09-09 v2 Probability
Spectral Theory
Abstract
In this paper we study the small scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is the coefficients take value with probability and with probability . Random waves whose coefficients are associated with a fair coin are known to equidistribute down to the wavelength scale. We obtain explicit requirements on the deviation from the fair () coin to retain equidistribution.
Cite
@article{arxiv.2103.08089,
title = {Small scale equidistribution of random waves generated by an unfair coin flip},
author = {Miriam Leonhardt and Melissa Tacy},
journal= {arXiv preprint arXiv:2103.08089},
year = {2021}
}
Comments
The previous version of the paper was missing some terms in the calculation of the variance. This version includes these terms, and is the final version. The method of the proof stays the same and the main results of the paper are unchanged