D-particles, matrix integrals and KP hierarchy

We study the regularized correlation functions of the light-like coordinate operators in the reduction to zero dimensions of the matrix model describi ng D-particles in four dimensions. We investigate in great detail the relat ed matrix model originally proposed and solved in the planar limit by J. Ho ppe. It also gives the solution of the problem of 3-coloring of planar grap hs. We find interesting strong/weak 't Hooft coupling dependence, The parti tion function of the grand canonical ensemble turns out to be a tau-functio n of KP hierarchy. As an illustration of the method we present a new deriva tion of the large-hr and double-scaling limits of the one-matrix model with cubic potential. (C) 1999 Published by Elsevier Science B.V, All rights re served.