Poissonian correlations of higher orders

Manuel Hauke; Agamemnon Zafeiropoulos

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arXiv · 2107.06523

Poissonian correlations of higher orders

Manuel Hauke·Agamemnon Zafeiropoulos

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Abstract

We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend connections between metric correlations and additive energy, already known for pair correlations, to higher orders. Furthermore, we examine how the property of Poissonian $k$-th correlations is reflected in the asymptotic size of the moments of the function $F(t,s,N) = #\{n\leq N : \|x_n - t\| \leq s/(2N) \},\, t\in [0,1]. $

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Manuel Hauke, Agamemnon Zafeiropoulos. 2021-07-14. Poissonian correlations of higher orders. https://arxiv.org/abs/2107.06523

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