An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval

Larcher, Gerhard; Puchhammer, Florian

doi:10.1515/udt-2016-0001

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An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval

Uniform distribution theory

Volume 11 (2016): Issue 1 (June 2016)

By: Gerhard Larcher and Florian Puchhammer

Open Access

|Jan 2017

Abstract

It is known that there is a constant c > 0 such that for every sequence x₁, x₂, . . . in [0, 1) we have for the star discrepancy $D_{N}^{*}$ $D_N^* $ of the first N elements of the sequence that ${ND}_{N}^{*} \geq c \cdot \log N$ $ND_N^* \ge c \cdot \log N$ holds for infinitely many N. Let c^∗ be the supremum of all such c with this property. We show c^∗ > 0.065664679 . . . , thereby slightly improving the estimates known until now.

References

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DOI: https://doi.org/10.1515/udt-2016-0001 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 1 - 14

Submitted on: Dec 1, 2014

Accepted on: Oct 2, 2015

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

uniform distribution,

discrepancy

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Gerhard Larcher, Florian Puchhammer, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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