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POINT DISTRIBUTIONS IN COMPACT METRIC SPACES

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

Published online by Cambridge University Press:  29 November 2017

M. M. Skriganov
M. M. Skriganov*
Affiliation:
St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia email maksim88138813@mail.ru
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Abstract

We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given (Theorem 1.1). We generalize Stolarsky’s invariance principle to distance-invariant spaces (Theorem 2.1). For arbitrary metric spaces, we prove a probabilistic invariance principle (Theorem 3.1). Furthermore, we construct equal-measure partitions of general rectifiable compact metric spaces into parts of small average diameter (Theorem 4.1).

MSC classification

Primary: 11K38: Irregularities of distribution, discrepancy 52C99: None of the above, but in this section

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Type
Research Article
Information
Mathematika , Volume 63 , Issue 3 , 2017 , pp. 1152 - 1171
Copyright
Copyright © University College London 2017 

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