Acta Mathematica Hungarica
Volume/Issue:
Volume 130: Issue 4
Extremal uniform distribution and random chord lengths
Author: Stefan Steinerberger 1
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  • 1 Institute for Financial Mathematics, Universität Linz, Altenbergstraße 69, A-4040 Linz, Austria
Pages:
321–339
Online Publication Date:
11 Jan 2011
Publication Date:
01 Mar 2011
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-0067-x
Keywords:
uniform distribution; random chord length; average distance; geometric probability; box integral; 11K06; 11J71; 41A10; 60D05
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Abstract

This paper generalizes earlier results on the behaviour of uniformly distributed sequences in the unit interval [0,1] to more general domains. We devote special attention to the most interesting special case [0,1]d. This will naturally lead to a problem in geometric probability theory, where we generalize results by Anderssen, Brent, Daley and Moran about random chord lengths in high-dimensional unit cubes, thereby answering a question by Bailey, Borwein and Crandall.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
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Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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