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arXiv · 1705.01327

The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals

Cheng-shi Liu
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Abstract

We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form functionals in the balls of continuous functions space with $p-$norm, and show the complete concentration of measure phenomenon which means that a functional takes its average on a ball with probability 1, from which we have nonlinear exchange formula of expectation.

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Cheng-shi Liu. 2017-05-03. The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals. https://arxiv.org/abs/1705.01327

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