Pair correlation and equidistribution on manifolds

Jens Marklof*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

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Abstract

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.
Original languageEnglish
Number of pages16
JournalMonatshefte für Mathematik
DOIs
Publication statusPublished - 17 Jun 2019

Keywords

  • Equidistribution
  • Pair correlation
  • Poisson process

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