Steepest descent method and limiting distributions in combinatorial analysis (Q1190475)

This article considers a class of combinatoric structures depending on a natural number \(n\) (such as permutation of \(n\) objects) and studies the probability distribution of a parameter of the structure (such as the number of cycles in a permutation). In particular results for the asymptotic probability distributions are considered. An extensive summary of the theorems and the underlying theory is given and this is followed by a long list of generating functions and the corresponding problems to which the theory can be applied.