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Matematicheskie Zametki, 2019, Volume 106, Issue 1, Pages 13–23
DOI: https://doi.org/10.4213/mzm12041 (Mi mzm12041) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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
Full-text PDF (658 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm12041
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.
Received: 13.04.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 1, Pages 11–19
DOI: https://doi.org/10.1134/S0001434619070022
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
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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\pages 13--23
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    • This publication is cited in the following 6 articles:
    1. Yuriy Dorn, Nikita Kornilov, Nikolay Kutuzov, Alexander Nazin, Eduard Gorbunov, Alexander Gasnikov, “Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits”, Comput Manag Sci, 21:1 (2024)  crossref  mathscinet
    2. Alexander Gasnikov, Darina Dvinskikh, Pavel Dvurechensky, Eduard Gorbunov, Aleksandr Beznosikov, Alexander Lobanov, Encyclopedia of Optimization, 2024, 1  crossref
    3. N. Kornilov, A. Gasnikov, P. Dvurechensky, D. Dvinskikh, “Gradient-free methods for non-smooth convex stochastic optimization with heavy-tailed noise on convex compact”, Comput. Manag. Sci., 20:1 (2023), 37  crossref  mathscinet
    4. E. Gorbunov, A. Rogozin, A. Beznosikov, D. Dvinskikh, A. Gasnikov, “Recent theoretical advances in decentralized distributed convex optimization”, High-Dimensional Optimization and Probability, Springer Optimization and Its Applications, 191, 2022, 253  crossref
    5. D. Dvinskikh, V. Tominin, I. Tominin, A. Gasnikov, “Noisy zeroth-order optimization for non-smooth saddle point problems”, Mathematical Optimization Theory and Operations Research, Lecture Notes in Computer Science, 13367, 2022, 18  crossref
    6. E. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, P. E. Dvurechenskii, “Accelerated gradient-free optimization methods with a non-Euclidean proximal operator”, Autom. Remote Control, 80:8 (2019), 1487–1501  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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