The distribution of spacings of real‐valued lacunary sequences modulo one

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2022Embargo end date: 01 Aug 2021 English Publisher:WileyJournal:Mathematika, volume 68, pages 416-428 (issn: 0025-5793, eissn: 2041-7942,

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Authors: Chaubey, Sneha; Yesha, Nadav;

doi: 10.1112/mtk.12129 , 10.48550/arxiv.2108.00431

arXiv: 2108.00431

The distribution of spacings of real‐valued lacunary sequences modulo one

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Abstract

Let $\left(a_{n}\right)_{n=1}^{\infty}$ be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all $α\in\mathbb{R}$, the pair correlation of $\left(αa_{n}\right)_{n=1}^{\infty}$ mod 1 is Poissonian. We show that all higher correlations and hence the nearest-neighbour spacing distribution are Poissonian as well, thereby extending a result of Rudnick and Zaharescu to real-valued sequences.

12 pages

Related Organizations

University of Haifa
Israel

Keywords

Probabilistic theory: distribution modulo $1$; metric theory of algorithms, Mathematics - Number Theory, FOS: Mathematics, lacunary sequences, Number Theory (math.NT), Poissonian nearest-neighbour spacing distribution, General theory of distribution modulo $1$

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