Minimal dispersion on the cube and the torus

We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random and non-random choice of points in the cube. This leads to b...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Arman, Andrii, Litvak, Alexander E
Format: Article
Language:English
Subjects:
Toruses
Upper bounds
Online Access:Get full text
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Summary:We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random and non-random choice of points in the cube. This leads to better upper bounds for the minimal dispersion.
ISSN:2331-8422