Matrix Model Combinatorics: Applications to Folding and Coloring
arXiv:math-ph/9911002
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".
69 pp, 24 figs, uses harvmac and epsf
References in corpus (5)
Cited by in corpus (12)
- Moments of the Gaussian Ensembles and the large- expansion of the densities
- Rectangular Matrix Models and Combinatorics of Colored Graphs
- Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
- Lectures on random matrix models. The Riemann-Hilbert approach
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Partial transpose of random quantum states: exact formulas and meanders
- Semiclassical treatment of quantum chaotic transport with a tunnel barrier
- Maximizing the number of edges in three-dimensional colored triangulations whose building blocks are balls
- Exactly solvable flat-foldable quadrilateral origami tilings
- Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders
- Semiclassical calculation of time delay statistics in chaotic quantum scattering
- Investigation of the two-cut phase region in the complex cubic ensemble of random matrices