Permanents in probability and statistics (Q908991)

If A is an \(n\times n\) matrix, then the permanent of A is defined as \(per\quad A=\sum_{\sigma \in S_ n}\prod^{n}_{i=1}a_{i\sigma (i)}\) where \(S_ n\) is the set of permutations of 1,2,...,n. Thus the definition of the permanent is similar to that of the determinant except that all terms in the expansion get a positive sign. A general survey of applications of the role of permanents in probability and statistics is made in the following areas: multiparameter versions of the multinomial and the negative multinomial distributions, log-concave sequences, order statistics for non-identically distributed random variables and sequential experiments. Some examples of Alexandroff's inequality are also discussed.