A General Asymptotic Scheme for Moments of Partition Statistics

Abstract

In the analysis of partition statistics, in particular if one is interested in means, variances or higher moments, one often has to deal with generating functions of the form P(x)F(x), where P(x) is the generating function for the number of partitions. The aim of this talk is to discuss a general asymptotic scheme that allows one to determine asymptotic expansions for the coefficients of such a generating function in a quasi-automatic way from expansions of F(x) around x = 1. In a certain sense, this scheme is a hybrid of the saddle point method and singularity analysis. The method is applicable to a wide variety of natural examples, and in some cases, it leads to surprisingly strong asymptotic results.