Discrepancy Theory

✍ Scribed by Dmitriy Bilyk (editor); Josef Dick (editor); Friedrich Pillichshammer (editor)

• Publisher: De Gruyter
• Year: 2020
• Tongue: English
• Leaves: 228
• Series: Radon Series on Computational and Applied Mathematics; 26
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Preface
Contents
1. On some recent developments in uniform distribution and discrepancy theory
2. Results and problems old and new in discrepancy theory
3. On negatively dependent sampling schemes, variance reduction, and probabilistic upper discrepancy bounds
4. Recent advances in higher order quasi-Monte Carlo methods
5. On the asymptotic behavior of the sine productΠⁿ_{r =1} /2 sin πrα/
6. Fibonacci lattices have minimal dispersion on the two-dimensional torus
7. On pair correlation of sequences
8. Some of Jiří Matoušek’s contributions to combinatorial discrepancy theory
9. Fourier analytic techniques for lattice point discrepancy