Moscow Mathematical Journal

Volume 21, Issue 4, October–December 2021 pp. 737–766.

Hypergraph Matrix Models

Authors: Mario DeFranco (1) and Paul E. Gunnells (2)
Author institution:(1) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305
(2) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305

Summary:

The classical GUE matrix model of $N\times N$ 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 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.

2020 Math. Subj. Class. Primary: 81T18, 16W10.

Keywords: Matrix models, hypergraphs, hyperbaggraphs.

Contents Full-Text PDF