# 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

arXiv: https://arxiv.org/abs/1804.03722 · HTML: https://mlsanity.com/paper/1804.03722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits](https://mlsanity.com/paper/2305.06743/) (2023)

## Abstract (arXiv)

We considered the problem of obtaining upper bounds for the mathematical expectation of the q-norm (2leqslant q leqslant ∞) of the vector which is uniformly distributed on the unit Euclidean sphere. We finish the paper with numerical experiments illustrating our results.