A Method of Moments for Random Recursive Structures

Abstract

I will present a method of moments useful for deriving the limiting distribution of recursively defined random variables. This classical approach, when applying to recursive random variables, necessitates the development of new tools called "asymptotic transfers," which roughly bridge the asymptotics of subproblems to that of the original problem. More than a dozen of examples in discrete probability, in analysis of algorithms, in random trees, will be used to illustrate the usefulness of this method. I will also mention recent progress of refining this method to get convergence rates and local limit theorems.