Properties of loop equations for the Hermitean matrix model and for two-dimensional quantum gravity

We study properties of the loop equations for the NxN Hermitean matrix model with arbitrary (even) interaction as well as of their continuum limit, associated with the two-dimensional quantum gravity. We apply the general procedure of iterative solution proposed recently by David. We relate the specific heat to the singular behavior of the connected correlator of two loops. We solve the continuum equation to a few lower orders in the string coupling constant, obtaining results for macroscopic loops, including the case of a multicritical fixed point. (orig.)