Point distributions in compact metric spaces, II

2017/01/15 by M. M. Skriganov, Skriganov, M. M.
Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1701.04007

openalex publication_date 2017/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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). This version of the paper will be published in Mathematika

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