Statistical distributions on integer partitions

In this talk we examine three types of distributions on integer partitions. (1) Generalizing a classical theorem of Erdos and Lehner, we determine the distribution of parts in partitions that are multiples of a fixed integer A. These limiting distributions are of Gumbel type, which are used to predict earthquakes! These results have implications in the algebraic geometry of n point Hilbert schemes. (2) For a fixed positive integer t, we determine the distribution of the number of hook lengths of size t among the partitions of n. As n tends to infinity, the distributions are asymptotically normal. (3) For a fixed integer t > 3, we determine the distribution of the number of hook lengths that are multiples of t among the partitions of n. As n tends to infinity, the distributions are asymptotically shifted Gamma distributions. This is joint work with Michael Griffin, Ken Ono, and Larry Rolen.