A lower bound for the dispersion on the torus

Mario Ullrich

doi:10.1016/j.matcom.2015.12.005

A lower bound for the dispersion on the torus

Mario Ullrich

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the volume of the largest axis-parallel box in the $d$-dimensional torus that contains no point of a given point set ${\cal P}_n$ with $n$ elements. We prove that, for all natural numbers $d,n$ and every point set ${\cal P}_n$, this volume is bounded from below by $min\{1,d/n\}$.This implies the same lower bound for the discrepancy on the torus.

Original language	English
Pages (from-to)	186-190
Number of pages	5
Journal	Mathematics and Computers in Simulation
Volume	143
Issue number	143
DOIs	https://doi.org/10.1016/j.matcom.2015.12.005
Publication status	Published - Jan 2018

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Computation in Informatics and Mathematics

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10.1016/j.matcom.2015.12.005

Cite this

@article{12644942d1664e8badc098b1d11ecf39,

title = "A lower bound for the dispersion on the torus",

abstract = "We consider the volume of the largest axis-parallel box in the \$d\$-dimensional torus that contains no point of a given point set \$\{\textbackslash{}cal P\}\_n\$ with \$n\$ elements. We prove that, for all natural numbers \$d,n\$ and every point set \$\{\textbackslash{}cal P\}\_n\$, this volume is bounded from below by \$min\textbackslash{}\{1,d/n\textbackslash{}\}\$.This implies the same lower bound for the discrepancy on the torus.",

author = "Mario Ullrich",

year = "2018",

month = jan,

doi = "10.1016/j.matcom.2015.12.005",

language = "English",

volume = "143",

pages = "186--190",

journal = "Mathematics and Computers in Simulation",

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AU - Ullrich, Mario

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AB - We consider the volume of the largest axis-parallel box in the $d$-dimensional torus that contains no point of a given point set ${\cal P}_n$ with $n$ elements. We prove that, for all natural numbers $d,n$ and every point set ${\cal P}_n$, this volume is bounded from below by $min\{1,d/n\}$.This implies the same lower bound for the discrepancy on the torus.

UR - https://www.scopus.com/pages/publications/84970016801

U2 - 10.1016/j.matcom.2015.12.005

DO - 10.1016/j.matcom.2015.12.005

M3 - Article

SN - 1872-7166

VL - 143

SP - 186

EP - 190

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 143

ER -

A lower bound for the dispersion on the torus

Abstract

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