A Panorama Of Discrepancy Theory
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A Panorama of Discrepancy Theory
This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.
Number Theory, Fourier Analysis and Geometric Discrepancy
Author: Giancarlo Travaglini
language: en
Publisher: Cambridge University Press
Release Date: 2014-06-12
Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.
Discrepancy Theory
Author: Dmitriy Bilyk
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2020-01-20
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.