Matrix Model Combinatorics: Applications to Folding and Coloring

1999/11/02 by P. Di Francesco, Di Francesco, P.
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th #math-ph #math.CO #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9911002

69 pp, 24 figs, uses harvmac and epsf

arxiv created 1999/11/02 · arxiv updated 2009/11/30

Abstract

We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these to the study of various folding problems arising from physics, including: the meander (or polymer folding) problem ``enumeration of all topologically inequivalent closed non-intersecting plane curves intersecting a line through a given number of points" and a fluid membrane folding problem reformulated as that of ``enumerating all vertex-tricolored triangulations of arbitrary genus, with given numbers of vertices of either color".

Related

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• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• A Diagrammatic Approach to the Meander Problem
• Combinatorial aspects of matrix models
• Supersymmetric Matrix Models and the Meander Problem