An enhanced uncertainty principle for the Vaserstein distance
Classical Analysis and ODEs
2021-06-29 v3
Abstract
We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function with mean zero, either the size of the zero set of the function or the cost of transporting the mass of the positive part of to its negative part must be big. We also provide a sharp upper estimate of the transport cost of the positive part of an eigenfunction of the Laplacian. This proves a conjecture of Steinerberger and provides a lower bound of the size of the nodal set of the eigenfunction.
Keywords
Cite
@article{arxiv.2003.03165,
title = {An enhanced uncertainty principle for the Vaserstein distance},
author = {Tom Carroll and Xavier Massaneda and Joaquim Ortega-Cerdà},
journal= {arXiv preprint arXiv:2003.03165},
year = {2021}
}
Comments
Corrected the argument at the proof of Theorem 1