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Mat. Zametki, 2019, Volume 106, Issue 1, Pages 13–23 (Mi mz12041)  

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

E. A. Gorbunova, E. Vorontsovabc, A. V. Gasnikovad

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Far Eastern Federal University, Vladivostok
c Université Grenoble Alpes
d Caucasus Mathematical Center, Adyghe State University, Maikop

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.

Keywords: concentration of measure, vector uniformly distributed on the sphere.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МД-1320.2018.1
Russian Foundation for Basic Research 18-31-20005 мол_а_вед
18-29-03071
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.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12041

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English version:
Mathematical Notes, 2019, 106:1, 11–19

Bibliographic databases:

UDC: 519.21
Received: 13.04.2018

Citation: E. A. Gorbunov, E. Vorontsova, A. V. Gasnikov, “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”, Mat. Zametki, 106:1 (2019), 13–23; Math. Notes, 106:1 (2019), 11–19

Citation in format AMSBIB
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\paper 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
\jour Mat. Zametki
\yr 2019
\vol 106
\issue 1
\pages 13--23
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\crossref{https://doi.org/10.4213/mzm12041}
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\jour Math. Notes
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