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On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere

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Abstract

We consider the problem of constructing upper bounds for the expectation of the norm of a vector uniformly distributed on the Euclidean unit sphere.

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Acknowledgments

The authors wish to express gratitude to P. E. Dvurechensky for his help.

Funding

The work of A. V. Gasnikov was supported by the Program of the President of the Russian Federation under grant MD-1320.2018.1. The work of È. A. Gorbunov was supported by the Russian Foundation for Basic Research under grant 18-31-20005 mol_a_ved. The work of E. A. Vorontsova was supported by the Russian Foundation for Basic Research under grant 18-29-03071.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow Oblast, 141701, Russia

    É. A. Gorbunov & A. V. Gasnikov

  2. Far Eastern Federal University, Vladivostok, 690950, Russia

    E. A. Vorontsova

  3. Université Grenoble Alpes, Grenoble, 38400, France

    E. A. Vorontsova

  4. Caucasus Mathematical Center, Adyghe State University, Maikop, 385000, Russia

    A. V. Gasnikov

Authors
  1. É. A. Gorbunov
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  2. E. A. Vorontsova
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  3. A. V. Gasnikov
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Corresponding authors

Correspondence to É. A. Gorbunov, E. A. Vorontsova or A. V. Gasnikov.

Additional information

Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 1, pp. 13–23.

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Gorbunov, É.A., Vorontsova, E.A. & Gasnikov, A.V. On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere. Math Notes 106, 11–19 (2019). https://doi.org/10.1134/S0001434619070022

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  • DOI: https://doi.org/10.1134/S0001434619070022

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