Niederreiter和Halton序列的配对相关不是Poissonian的
Pair Correlations of Niederreiter and Halton Sequences are not Poissonian
摘要：
Niederreiter序列和Halton序列是两类重要的多维序列，由于其优良的分布特性，在实际的数值积分方法中得到了广泛的应用。在本文中，我们表明，这些序列-即使它们是均匀分布的-不能满足泊松对相关性的较强的属性。这扩展了已经建立的一维序列的结果，并证实了一个猜想的拉彻和Stockinger。证明依赖于一个通用的工具，该工具确定特定的序列不具有泊松对相关性是足够的。
英文摘要：
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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