Geometric Discrepancy: An Illustrated Guide

前表紙
Jiri Matousek
Springer Science & Business Media, 1999/05/19 - 289 ページ
Discrepancy theory is also called the theory of irregularities of distribution. Here are some typical questions: What is the "most uniform" way of dis tributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? For a precise formulation of these questions, we must quantify the irregularity of a given distribution, and discrepancy is a numerical parameter of a point set serving this purpose. Such questions were first tackled in the thirties, with a motivation com ing from number theory. A more or less satisfactory solution of the basic discrepancy problem in the plane was completed in the late sixties, and the analogous higher-dimensional problem is far from solved even today. In the meantime, discrepancy theory blossomed into a field of remarkable breadth and diversity. There are subfields closely connected to the original number theoretic roots of discrepancy theory, areas related to Ramsey theory and to hypergraphs, and also results supporting eminently practical methods and algorithms for numerical integration and similar tasks. The applications in clude financial calculations, computer graphics, and computational physics, just to name a few. This book is an introductory textbook on discrepancy theory. It should be accessible to early graduate students of mathematics or theoretical computer science. At the same time, about half of the book consists of material that up until now was only available in original research papers or in various surveys.
 

目次

III
1
V
9
VII
16
VIII
22
IX
37
X
38
XI
44
XII
51
XXVII
145
XXVIII
155
XXIX
159
XXX
164
XXXI
171
XXXII
172
XXXIII
176
XXXIV
180

XIII
61
XIV
72
XV
83
XVI
84
XVII
93
XVIII
101
XX
105
XXI
109
XXII
117
XXIII
120
XXIV
128
XXV
137
XXXV
182
XXXVI
193
XXXVII
197
XXXVIII
203
XXXIX
213
XLI
230
XLII
234
XLIII
241
XLIV
245
XLV
265
XLVI
275
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人気のある引用

246 ページ - H. Bronnimann, B. Chazelle and J. Matousek, Product Range Spaces, Sensitive Sampling, and Derandomization, Proc.
255 ページ - In press, (ref: p. 38) [KPW92] J. Komlos, J. Pach, and G. Woeginger. Almost tight bounds for e-nets. Discrete Comput. Geom., 7:163-173, 1992.

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