Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces
- 1 March 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (1) , 221-228
- https://doi.org/10.2307/3213932
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
This publication has 6 references indexed in Scilit:
- The volume of a random simplex in an n-ball is asymptotically normalJournal of Applied Probability, 1977
- Limit Distributions of Self-normalized SumsThe Annals of Probability, 1973
- Asymptotical independence of the lengths of subintervals of a randomly partitioned interval; a sample from S. Ikeda's workStatistica Neerlandica, 1969
- Asymptotic ExpansionsPublished by Cambridge University Press (CUP) ,1965
- The Distribution of Distance in a HypersphereThe Annals of Mathematical Statistics, 1954
- The Distribution of Distance in a HypersphereThe Annals of Mathematical Statistics, 1950