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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 3, Pages 501–516 (Mi tvp91)  

This article is cited in 4 scientific papers (total in 4 papers)

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

V. I. Khokhlov

Steklov Mathematical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/tvp91

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English version:
Theory of Probability and its Applications, 2006, 50:3, 386–399

Bibliographic databases:

Received: 03.07.2005

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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    2. Alvarez F., Lippi F., “Price Setting With Menu Cost For Multiproduct Firms”, Econometrica, 82:1 (2014), 89–135  crossref  mathscinet  zmath  isi  elib  scopus
    3. O. V. Viskov, V. I. Khokhlov, “Four areas of Yu. V. Prokhorov's studies and their perspectives”, Theory Probab. Appl., 60:2 (2016), 336–342  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Ahmadi-Javid A., Moeini A., “Uniform Distributions and Random Variate Generation Over Generalized l(P) Balls and Spheres”, J. Stat. Plan. Infer., 201 (2019), 1–19  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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