A remark on the minimal dispersion
A.E. Litvak
TL;DR
This paper enhances upper bounds for the minimal dispersion of point sets in the unit cube, providing sharper estimates in both periodic and non-periodic contexts, with some bounds being nearly optimal.
Contribution
It introduces improved bounds for minimal dispersion, advancing the theoretical understanding of point set distributions in high-dimensional cubes.
Findings
New upper bounds for minimal dispersion in periodic and non-periodic settings
Some bounds are proven to be nearly sharp, up to logarithmic factors
Advances the theoretical limits of point set uniformity in the unit cube
Abstract
We improve known 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. Some of our bounds are sharp up to logarithmic factors.
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Taxonomy
TopicsMathematical Approximation and Integration · Machine Learning and Algorithms · Electromagnetic Scattering and Analysis