发表机构
TU Graz（格拉茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个同时具有低差异性和泊松配对相关性的序列，解决了此前认为这两种性质不可调和的猜想。
AI 中文摘要
模1均匀分布是单位区间内序列伪随机性的经典概念，其量化通过差异度进行。差异度达到最小可能渐近阶的序列被称为低差异序列。泊松配对相关性是另一种伪随机性概念，它研究序列元素对之间间隙在局部尺度上的分布。已知泊松配对相关性蕴含模1均匀分布，而反向蕴含一般不成立。也已观察到经典的低差异序列例子不具备泊松配对相关性，且有人推测由于低差异行为所需的高度结构刚性，这两种性质可能不可调和。正如我们在本文中所证明的，情况并非如此：我们构造了一个具有泊松配对相关性的低差异序列的例子。
英文摘要
Uniform distribution modulo 1 is a classical notion of pseudo-randomness for sequences in the unit interval, which is quantified in terms of the discrepancy. Sequences whose discrepancy is of the smallest possible asymptotic order are called low-discrepancy sequences. The Poissonian pair correlation is another notion of pseudo-randomness, which studies the distribution of the gaps between pairs of elements of the sequence on a local scale. It is known that Poissonian pair correlation implies uniform distribution mod 1, and that the opposite implication is not true in general. It has also been observed that classical examples of low-discrepancy sequences fail to have Poissonian pair correlation, and it has been speculated that the two properties might be irreconcilable due to the high degree of structural rigidity that is required for low-discrepancy behavior. As we prove in this paper, this is not the case: we construct an example of a low-discrepancy sequence with Poissonian pair correlation.
Comments22 pages. Comments are welcome
