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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

Authors
  • Gorbunov, É. A.1
  • Vorontsova, E. A.2, 3
  • Gasnikov, A. V.1, 4
  • 1 Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow Oblast, 141701, Russia , Dolgoprudnyi, Moscow Oblast (Russia)
  • 2 Far Eastern Federal University, Vladivostok, 690950, Russia , Vladivostok (Russia)
  • 3 Université Grenoble Alpes, Grenoble, 38400, France , Grenoble (France)
  • 4 Adyghe State University, Caucasus Mathematical Center, Maikop, 385000, Russia , Maikop (Russia)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
Jul 01, 2019
Volume
106
Issue
1-2
Pages
11–19
Identifiers
DOI: 10.1134/S0001434619070022
Source
Springer Nature
Keywords
License
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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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