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Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces

Published online by Cambridge University Press:  14 July 2016

A. J. Stam
A. J. Stam*
Affiliation:
Rijksuniversiteit Groningen
*
∗Postal address: Mathematisch Instituut Rijksuniversiteit, Postbus 800, 9700AV Groningen, The Netherlands.
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Abstract

If X = (X1, · ··, Xn) has uniform distribution on the sphere or ball in ℝ with radius a, then the joint distribution of , ···, k, converges in total variation to the standard normal distribution on ℝ. Similar results hold for the inner products of independent n-vectors. Applications to geometric probability are given.

Keywords

CENTRAL LIMIT THEOREMUNIFORM DISTRIBUTIONGEOMETRIC PROBABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 221 - 228
Copyright
Copyright © Applied Probability Trust 1982 

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