Chapter
Licensed
Unlicensed
Requires Authentication
2. Results and problems old and new in discrepancy theory
-
W. W. L. Chen
Abstract
In this brief survey, we discuss some of the main results in discrepancy theory and highlight many of the very difficult open problems that remain in the subject.
You are currently not able to access this content.
Abstract
In this brief survey, we discuss some of the main results in discrepancy theory and highlight many of the very difficult open problems that remain in the subject.
You are currently not able to access this content.
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1. On some recent developments in uniform distribution and discrepancy theory 1
- 2. Results and problems old and new in discrepancy theory 21
- 3. On negatively dependent sampling schemes, variance reduction, and probabilistic upper discrepancy bounds 43
- 4. Recent advances in higher order quasi-Monte Carlo methods 69
- 5. On the asymptotic behavior of the sine productΠnr =1 /2 sin πrα/ 103
- 6. Fibonacci lattices have minimal dispersion on the two-dimensional torus 117
- 7. On pair correlation of sequences 133
- 8. Some of Jiří Matoušek’s contributions to combinatorial discrepancy theory 147
- 9. Fourier analytic techniques for lattice point discrepancy 173
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1. On some recent developments in uniform distribution and discrepancy theory 1
- 2. Results and problems old and new in discrepancy theory 21
- 3. On negatively dependent sampling schemes, variance reduction, and probabilistic upper discrepancy bounds 43
- 4. Recent advances in higher order quasi-Monte Carlo methods 69
- 5. On the asymptotic behavior of the sine productΠnr =1 /2 sin πrα/ 103
- 6. Fibonacci lattices have minimal dispersion on the two-dimensional torus 117
- 7. On pair correlation of sequences 133
- 8. Some of Jiří Matoušek’s contributions to combinatorial discrepancy theory 147
- 9. Fourier analytic techniques for lattice point discrepancy 173
