1. 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
- Author
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Eduard Gorbunov, Alexander Gasnikov, Evgeniya Vorontsova, Moscow Institute of Physics and Technology [Moscow] (MIPT), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Far Eastern Federal University (FEFU)
- Subjects
Unit sphere ,Concentration of measure ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,MathematicsofComputing_GENERAL ,02 engineering and technology ,16. Peace & justice ,равномерно распределённый насфере вектор ,01 natural sciences ,Measure (mathematics) ,Upper and lower bounds ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Optimization and Control (math.OC) ,Phenomenon ,Euclidean geometry ,FOS: Mathematics ,Mathematics::Metric Geometry ,концентрация меры ,0101 mathematics ,[MATH]Mathematics [math] ,Mathematics - Optimization and Control ,Mathematics - Abstract
We considered the problem of obtaining upper bounds for the mathematical expectation of the $q$-norm ($2\leqslant q \leqslant \infty$) of the vector which is uniformly distributed on the unit Euclidean sphere. We finish the paper with numerical experiments illustrating our results., Comment: in Russian, 10 pages, 2 figures
- Published
- 2019