  We study several-matrix models and show that when the potential is convex and
a small perturbation of the Gaussian potential, the first order correction to
the free energy can be expressed as a generating function for the enumeration
of maps of genus one. In order to do that, we prove a central limit theorem for
traces of words of the weakly interacting random matrices defined by these
matrix models and show that the variance is a generating function for the
number of planar maps with two vertices with prescribed colored edges.
