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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 ÌÄ-1320.2018.1 Russian Foundation for Basic Research 18-31-20005 ìîë_à_âåä18-29-03071 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

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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