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Pair correlation and equidistribution on manifolds

Research output: Contribution to journalArticle

Original languageEnglish
Number of pages16
JournalMonatshefte für Mathematik
DateAccepted/In press - 6 Jun 2019
DatePublished (current) - 17 Jun 2019


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.

    Research areas

  • Equidistribution, Pair correlation, Poisson process

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