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The volume of a random simplex in an n-ball is asymptotically normal

Published online by Cambridge University Press:  14 July 2016

Harold Ruben
Harold Ruben*
Affiliation:
McGill University, Montreal
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Abstract

A proof is given of a conjecture in the literature of geometrical probability that the r-content of the r-simplex whose r + 1 vertices are independent random points of which p are uniform in the interior and q uniform on the boundary of a unit n-ball (1 ≦ r ≦ n; 0 ≦ p, q ≦ r + 1, p + q = r + 1) is asymptotically normal (n →∞) with asymptotic mean and variance and , respectively.

Keywords

BLASCHKE-PETKANTSCHIN REPRESENTATIONCOMPLEX MOMENTS OF r-VOLUME OF RANDOM r-SIMPLEX IN n-BALLDIFFERENCE EQUATIONCHARACTERISTIC FUNCTION OF LOGARITHM OF VOLUMEASYMPTOTIC NORMALITY OF VOLUME
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 647 - 653
Copyright
Copyright © Applied Probability Trust 1977 

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References

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