Geodesic
The uniform distribytion on sphere in $R^s$. I. Properties of projections
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 501-516 Cet article a éte moissonné depuis la source Math-Net.Ru

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The distribution law of the first $k$ coordinates of a point uniformly distributed over a high dimensional sphere and the distribution law of $k$ independent standard normal variables, as $n\to\infty$ with $k$ fixed, are considered. The main result of this paper is a lower bound on the variational distance. The well-known upper bound due to Diaconis and Freedman has been made more precise.
Mots-clés : variational distance
Keywords: uniform distribution on a sphere. 
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V. I. Khokhlov. The uniform distribytion on sphere in $R^s$. I. Properties of projections. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 501-516. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a4/

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