On the upper bound for the mathematical expectation of the norm of a vector uniformly distributed on the sphere and the phenomenon of concentration of uniform measure on the sphere

Eduard Gorbunov; Evgeniya Vorontsova; Alexander Gasnikov

doi:10.1134/s0001434619070022

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arXiv · 1804.03722

On the upper bound for the mathematical expectation of the norm of a vector uniformly distributed on the sphere and the phenomenon of concentration of uniform measure on the sphere

Eduard Gorbunov·Evgeniya Vorontsova·Alexander Gasnikov

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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.

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Eduard Gorbunov, Evgeniya Vorontsova, Alexander Gasnikov. 2018-04-10. On the upper bound for the mathematical expectation of the norm of a vector uniformly distributed on the sphere and the phenomenon of concentration of uniform measure on the sphere. https://doi.org/10.1134/s0001434619070022

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