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arXiv · 1908.11147

Pair Correlations of Niederreiter and Halton Sequences are not Poissonian

Roswitha Hofer·Lisa Kaltenböck
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Abstract

Niederreiter and Halton sequences are two prominent classes of multi-dimensional sequences which are widely used in practice for numerical integration methods because of their excellent distribution qualities. In this paper, we show that these sequences - even though they are uniformly distributed - fail to satisfy the stronger property of Poissonian pair correlations. This extends already established results for one-dimensional sequences and confirms a conjecture of Larcher and Stockinger. The proofs rely on a general tool which identifies specific regularities of a sequence to be sufficient for not having Poissonian pair correlations.

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Roswitha Hofer, Lisa Kaltenböck. 2019-08-29. Pair Correlations of Niederreiter and Halton Sequences are not Poissonian. https://arxiv.org/abs/1908.11147

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