An introduction to discrepancy theory
Date
2019-08-01
Authors
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Journal ISSN
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Abstract
This paper introduces the basic elements of geometric discrepancy theory. After some background we discuss lower bounds for two problems, Schmidt’s theorem giving a lower bound for convex sets and Roth’s orthogonal method for the lower bound of the L₂ discrepancy of axis-parallel rectangles in the unit square. Then we introduce two sets with low worst-case discrepancy, the Van der Corput set for two dimensions and the Halton-Hammersley set for arbitrary dimension.
Description
Keywords
Discrepancy theory
Graduation Month
August
Degree
Master of Science
Department
Department of Mathematics
Major Professor
Craig Spencer
Date
2019
Type
Report