Speaker: Virgil Pierce
Title: Random Matrices and Map Enumeration
Abstract: We have been considering a partition function of random matrices represented by the Gaussian expectation of a unitary invariant function over N x N Hermitian matrices. The particular choice of invariant function we use gives a Partition Function whose large N asymptotic expansion is a counting function for Maps (a type of labeled graph). This fact can be formally motivated by use of the Wick Lemma for Gaussian expectations. We will then explore two interpretations of Maps: a complex analysis definition, and a group theory version.