2019/03/02 by Jens Marklof, Marklof, Jens · 2 citations
Computer Science · Mathematics · #11K06 #11K45 #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Point processes and geometric inequalities #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1903.00670
openalex publication_date 2019/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been proved for point sequences on higher-dimensional tori. The purpose of this paper is to describe a simple statistical argument that explains this observation and furthermore permits a generalisation to bounded Euclidean domains as well as compact Riemannian manifolds.