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Random circles in the d-dimensional unit ball

Published online by Cambridge University Press:  14 July 2016

Fernando Affentranger
Fernando Affentranger*
Affiliation:
Universidad de Buenos Aires
*
∗ Present address: Mathematisches Institut, Albert-Ludwigs-Universität, Albertstrasse 23B, D-7800 Freiburg im Br., W. Germany.
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Abstract

This note gives the solution of the following problem concerning geometric probabilities. What is the probability p(Bd; 2) that the circumference determined by three points P, P1 and P2 chosen independently and uniformly at random in the interior of a d-dimensional unit ball Bd in Euclidean space Ed (d ≧ 2) is entirely contained in Bd? From our result we conclude that p(Bd; 2) →π /(3√3) as d →∞.

Keywords

GEOMETRY OF THE d-BALLGEOMETRICAL PROBABILITYINTEGRAL GEOMETRYRANDOM SET OF POINTSSTOCHASTIC GEOMETRY
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 408 - 412
Copyright
Copyright © Applied Probability Trust 1989 

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