On a multi-dimensional Poissonian pair correlation concept and uniform distribution

Hinrichs, Aicke; Kaltenböck, Lisa; Larcher, Gerhard; Stockinger, Wolfgang; Ullrich, Mario

doi:10.48550/arxiv.1809.05672

Cited by 3 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The answer is yes, even under weaker hypotheses than (1.2), for sequences in the unit interval [1,8,18]. The same has been established for point sequences on higher-dimensional tori [10,19]. In the present paper we develop a statistical argument that permits a generalisation of these findings to bounded domains in R d (Section 2) as well as compact Riemannian manifolds (Section 3; the special case of flat tori is discussed in the appendix).…”

Section: Introductionmentioning

confidence: 63%

Pair correlation and equidistribution on manifolds

Marklof

2019

Monatsh Math

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 63%

Pair correlation and equidistribution on manifolds

Marklof

2019

Monatsh Math

View full text Add to dashboard Cite

show abstract

“…Theorem (Hinrichs, Kaltenböck, Larcher, Stockinger & Ullrich [8]). Let (x n ) ∞ n=1 be a sequence in [0, 1] d and assume that for all s > 0 lim…”

mentioning

confidence: 99%

Poissonian pair correlation in higher dimensions

Steinerberger

2020

Journal of Number Theory

View full text Add to dashboard Cite

show abstract

“…Of course it makes sense to generalize the concept of PPC to the multidimensional setting. One way to generalize the one-dimensional concept to a multi-dimensioanl setting was defined and discussed in [15] (for a more general analysis of a multi-dimensional PPC concept, we refer to the recent work [21]). Here, we present the definition of [15].…”

mentioning

confidence: 99%