Remarks on ``Coloring Random Triangulation''

TL;DR

This paper critiques previous results on coloring random triangulations by transforming a two-matrix model into a one-matrix model and demonstrating the unreliability of earlier resolvent and density calculations.

Contribution

It introduces a method to convert the two-matrix model into a proper one-matrix model and questions the validity of prior analytical results.

Findings

The two-matrix model can be transformed into a proper one-matrix model.

Previous results for resolvent and density are shown to be unreliable.

The method clarifies the limitations of earlier approaches.

Abstract

We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a ``formal'' integral used by these authors as a proper integral. We show also, using their method, that the results obtained for the resolvent and the density are not reliable.