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arXiv · 2108.00431

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

Sneha Chaubey·Nadav Yesha
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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 $\alpha\in\mathbb{R}$, the pair correlation of $\left(\alpha a_{n}\right)_{n=1}^{\infty}$ 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.

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Sneha Chaubey, Nadav Yesha. 2021-08-01. The distribution of spacings of real-valued lacunary sequences modulo one. https://arxiv.org/abs/2108.00431

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