New bounds on the minimal dispersion
Metric Geometry
2022-01-24 v3 Probability
Abstract
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in . This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings in certain regimes. Up to double logarithmic factor, our bounds are sharp. We also apply our construction to -dispersion.
Keywords
Cite
@article{arxiv.2108.10374,
title = {New bounds on the minimal dispersion},
author = {Alexander E. Litvak and Galyna V. Livshyts},
journal= {arXiv preprint arXiv:2108.10374},
year = {2022}
}
Comments
17 pages; final version uploaded