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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 3, Pages 501–516
DOI: https://doi.org/10.4213/tvp91 (Mi tvp91) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The uniform distribytion on sphere in $R^s$. I. Properties of projections

V. I. Khokhlov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (1004 kB) Citations (8)
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DOI: https://doi.org/10.4213/tvp91
Abstract: 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.
Keywords: variational distance, uniform distribution on a sphere.
Received: 03.07.2005
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 3, Pages 386–399
DOI: https://doi.org/10.1137/S0040585X97981846
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Khokhlov, “The uniform distribytion on sphere in $R^s$. I. Properties of projections”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 501–516; Theory Probab. Appl., 50:3 (2006), 386–399
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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