%0 Generic %1 liu2017geometrical %A Liu, Cheng-shi %D 2017 %K func-an maths thermod %T The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals %U http://arxiv.org/abs/1705.01327 %X 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.

@misc{liu2017geometrical, 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.}, added-at = {2017-05-04T23:46:41.000+0200}, author = {Liu, Cheng-shi}, biburl = {https://www.bibsonomy.org/bibtex/21f68f7e293af9d53f1f4de7527b7eaee/vindex10}, description = {The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals}, interhash = {a6b64566eed3a2c426fed1d3942dc67f}, intrahash = {1f68f7e293af9d53f1f4de7527b7eaee}, keywords = {func-an maths thermod}, note = {cite arxiv:1705.01327Comment: 8 pages}, timestamp = {2017-05-04T23:46:41.000+0200}, title = {The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals}, url = {http://arxiv.org/abs/1705.01327}, year = 2017 }