4.4 Article

Pair correlation and equidistribution on manifolds

Journal

MONATSHEFTE FUR MATHEMATIK
Volume 191, Issue 2, Pages 279-294

Publisher

SPRINGER WIEN
DOI: 10.1007/s00605-019-01308-3

Keywords

Pair correlation; Equidistribution; Poisson process

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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.

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