This seems to be a specific case of the more general principle of "concentration of measure". Terence Tao at [1] has some useful notes. From a quick scan of t

This seems to be a specific case of the more general principle of "concentration of measure". Terence Tao at [1] has some useful notes. From a quick scan of the paper at http://arxiv.org/pdf/1402.0423v1.pdf http://arxiv.org/pdf/1402.0423v1.pdf, Theorem 1 seems to essentially be a CoM result for the order statistics of symmetric RVs. This same principle can be applied in other contexts [2] - e.g. Johnson-Lindestrauss is essentially a statement that random projections are "often" nearly isometries. [1]: http://terrytao.wordpress.com/2010/01/03/254a-notes-1-concentration-of-measure/ http://terrytao.wordpress.com/2010/01/03/254a-notes-1-concen... [2]: https://news.ycombinator.com/item?id=7971188 https://news.ycombinator.com/item?id=7971188