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

2021/08/01 by Sneha Chaubey, Chaubey, Sneha, Nadav Yesha +1
Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.00431

openalex publication_date 2021/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (a_n)_n=1^∞ be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all α∈ℝ, the pair correlation of (αa_n)_n=1^∞ 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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