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Coloring Random Triangulations

P. Di Francesco·B. Eynard·E. Guitter
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Abstract

We introduce and solve a two-matrix model for the tri-coloring problem of the vertices of a random triangulation. We present three different solutions: (i) by orthogonal polynomial techniques (ii) by use of a discrete Hirota bilinear equation (iii) by direct expansion. The model is found to lie in the universality class of pure two-dimensional quantum gravity, despite the non-polynomiality of its potential.

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P. Di Francesco, B. Eynard, E. Guitter. 1997-11-06. Coloring Random Triangulations. https://doi.org/10.1016/s0550-3213(98)00037-6

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