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Acta Mathematica Hungarica

, Volume 130, Issue 4, pp 321–339 | Cite as

Extremal uniform distribution and random chord lengths

  • Stefan SteinerbergerEmail author
Article

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.

Key words and phrases

uniform distribution random chord length average distance geometric probability box integral 

2000 Mathematics Subject Classification

11K06 11J71 41A10 60D05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Institute for Financial MathematicsUniversität LinzLinzAustria

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