Chen / Srivastav / Travaglini A Panorama of Discrepancy Theory

Erscheinungsjahr 2014
ISBN: 978-3-319-04696-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2107, 695 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Chen, William

Srivastav, Anand

Travaglini, Giancarlo

Inhaltsverzeichnis

Preface.- Classical and Geometric Discrepancy.- Upper Bounds in Classical Discrepancy Theory.- Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections.- Irregularities of distribution and average decay of Fourier transforms.- Superirregularity.- Combinatorial Discrepancy.- Multicolor Discrepancy of Arithmetic Structures.- Algorithmic Aspects of Combinatorial Discrepancy.- Practical Algorithms for Low-Discrepancy 2-Colorings.- Applications and Constructions.- On the distribution of solutions to diophantine equations.- Discrepancy theory and quasi-Monte Carlo integration.- Calculation of Discrepancy Measures and Applications.- Author index.- Subject index