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This article is cited in 1 scientific paper (total in 1 paper)
Hypergraph matrix models
Mario DeFranco, Paul E. Gunnells Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305
Abstract:
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.
Key words and phrases:
matrix models, hypergraphs, hyperbaggraphs.
Citation:
Mario DeFranco, Paul E. Gunnells, “Hypergraph matrix models”, Mosc. Math. J., 21:4 (2021), 737–766
Linking options:
https://www.mathnet.ru/eng/mmj811 https://www.mathnet.ru/eng/mmj/v21/i4/p737
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Abstract page: | 53 | References: | 16 |
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