Genus Expansions of Hermitian One-Matrix Models: Fat Graphs vs. Thin Graphs

TL;DR

This paper compares two genus expansion methods for Hermitian one-matrix models, analyzing fat graphs and thin graphs, and establishes structural results for the thin graph approach before applying them to fat graphs.

Contribution

It introduces a structural analysis of genus expansions using renormalized coupling constants for thin graphs and applies these results to fat graphs.

Findings

Structural results for thin graph genus expansion

Application of thin graph results to fat graph expansion

Enhanced understanding of genus expansion structures

Abstract

We consider two different genus expansions of the free energy functions of Hermitian one-matrix models, one using fat graphs, one using ordinary graphs (thin graphs). Some structural results are first proved for the thin version of genus expansion using renormalized coupling constants, and then applied to the fat version.