Hypergraph Matrix Models

Abstract

The classical GUE matrix model of N×N Hermitian matrices equipped with the Gaussian measure can be used to count the orientable topological surfaces by genus obtained through gluing the edges of a polygon. We introduce a variation of the GUE matrix model that that enumerates certain edge-ramified CW complexes obtained from polygon gluings. We do this by replacing the Gaussian measure with a formal analogue related to generating functions that enumerate uniform hypergraphs. Our main results are three different ways to compute expectations of traces of powers. In particular, we show that our matrix model has a topological expansion.