Discrepancy Theory

Published by De Gruyter 2020

Discrepancy Theory

Edited by: Dmitriy Bilyk , Josef Dick and Friedrich Pillichshammer

Volume 26 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110652581

Overview
Contents

About this book

The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

A collection of surveys in discrepancy theory
Covers all related applications areas, including discrete mathematics, number theory, and computation
Includes contributions from leading experts in the field

Author / Editor information

D. Bilyk, Univ. of Minnesota, USA; J. Dick, Univ. of New South Wales, Australia; F. Pillichshammer, Johannes Kepler Univ. Linz, Austria.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	IX
1. On some recent developments in uniform distribution and discrepancy theory Dmitriy Bilyk Requires Authentication Unlicensed Licensed Download PDF	1
2. Results and problems old and new in discrepancy theory W. W. L. Chen Requires Authentication Unlicensed Licensed Download PDF	21
3. On negatively dependent sampling schemes, variance reduction, and probabilistic upper discrepancy bounds Marcin Wnuk, Michael Gnewuch and Nils Hebbinghaus Requires Authentication Unlicensed Licensed Download PDF	43
4. Recent advances in higher order quasi-Monte Carlo methods Takashi Goda and Kosuke Suzuki Requires Authentication Unlicensed Licensed Download PDF	69
5. On the asymptotic behavior of the sine productΠⁿ_{r =1} /2 sin πrα/ Sigrid Grepstad, Lisa Kaltenböck and Mario Neumüller Requires Authentication Unlicensed Licensed Download PDF	103
6. Fibonacci lattices have minimal dispersion on the two-dimensional torus Simon Breneis and Aicke Hinrichs Requires Authentication Unlicensed Licensed Download PDF	117
7. On pair correlation of sequences Gerhard Larcher and Wolfgang Stockinger Requires Authentication Unlicensed Licensed Download PDF	133
8. Some of Jiří Matoušek’s contributions to combinatorial discrepancy theory Aleksandar Nikolov Requires Authentication Unlicensed Licensed Download PDF	147
9. Fourier analytic techniques for lattice point discrepancy Luca Brandolini and Giancarlo Travaglini Requires Authentication Unlicensed Licensed Download PDF	173

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in discrete and computational mathematics.
Pages
- Front matter: 9
- Main content: 216
Illustrations
- Illustrations: 30
Keywords: Diskrepanz; Dispersion; Korrelation; Monte-Carlo-Integration; Wahrscheinlichkeitsverteilung

eBook

Published: January 20, 2020
ISBN: 9783110652581

Hardcover

Published: January 20, 2020
ISBN: 9783110651157