Pair correlation and equidistribution on manifolds

Jens Marklof

doi:10.1007/s00605-019-01308-3

Pair correlation and equidistribution on manifolds

Jens Marklof^*

^*Corresponding author for this work

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14 Citations (Scopus)

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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 language	English
Number of pages	16
Journal	Monatshefte für Mathematik
DOIs	https://doi.org/10.1007/s00605-019-01308-3
Publication status	Published - 17 Jun 2019

Keywords

Equidistribution
Pair correlation
Poisson process

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AB - 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.

KW - Equidistribution

KW - Pair correlation

KW - Poisson process

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DO - 10.1007/s00605-019-01308-3

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ER -

Pair correlation and equidistribution on manifolds

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