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Irregularities of distributions with respect to polytopes

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  26 February 2010

Michael Drmota
Michael Drmota
Affiliation:
Department of Discrete Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/118, A-1040 Vienna, Austria.
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Abstract

In the first part of the paper we show that the L2-discrepancy with respect to squares is of the same order of magnitude as the usual L2- discrepancy for point distributions in the K-dimensional torus. In the second part we adapt this method to obtain a generalization of Roth's [7] lower bound (log N)(k-1)/2 (for the usual discrepancy) to the discrepancy with respect to homothetic simple convex poly topes.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 108 - 119
Copyright
Copyright © University College London 1996

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References

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