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

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.

References in corpus (3)

• Emergent Geometry and Mirror Symmetry of A Point
• On Topological 1D Gravity. I
• Hermitian One-Matrix Model and KP Hierarchy

Cited by in corpus (5)

• Grothendieck's Dessins d'Enfants in a Web of Dualities. II
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Fat and Thin Emergent Geometries of Hermitian One-Matrix Models
• A formalism of abstract quantum field theory of summation of fat graphs
• Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$