EXACT SOLUTION OF THE O(N) MODEL ON A RANDOM LATTICE

We present an exact solution of the O(n) model on a random lattice. Th e coupling constant space of our model is parametrized in terms of a s et of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In add ition we find a large degree of universality with respect to n; namely for n is an element of]] - 2,2[ the solution can be presented in a fo rm which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = +/-2 are treated separately. We g ive explicit expressions for the genus-zero contribution to the one- a nd two-loop correlators as well as for the genus-one contribution to t he one-loop correlator and the free energy. It is shown how one can ob tain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is d escribed, Furthermore we describe how the calculation of the higher-ge nera contributions can be pursued in the scaling limit.