Stochastic rearrangement inequalities (Q1093984)

From authors' introduction: ``Rearrangement inequalities compare the value of a function of vector arguments with the value of the same function after the components of the vectors have been rearranged. The well-known rearrangement inequality of \textit{G. H. Hardy, J. E. Littlewood} and \textit{G. Pólya} [Inequalities. 2nd ed., Cambridge (1952); for a review of the first edition see Zbl 0010.10703)] states that if \(x=(x_ 1,...,x_ n)\) and \(y=(y_ 1,...,y_ n)\) are vectors of nonnegative, increasing components and \(\pi =(\pi (1),...,\pi (n))\) is any permutation, then \[ \sum^{n}_{i=1}x_ iy_ i\geq \sum^{n}_{i=1}x_ iy_{\pi (i)}\geq \sum^{n}_{i=1}x_ iy_{n-i+1}. \] In this paper we develop a general theory for obtaining stochastic versions of results of this nature.'' ``In Sections 5 and 6 we present some illustrative applications of the theory to ranking problems, hypothesis testing problems, and contamination models.''