Pair correlation and equidistribution on manifolds

Jens Marklof*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
174 Downloads (Pure)


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
Publication statusPublished - 17 Jun 2019


  • Equidistribution
  • Pair correlation
  • Poisson process


Dive into the research topics of 'Pair correlation and equidistribution on manifolds'. Together they form a unique fingerprint.

Cite this