D-particles, Matrix Integrals and KP hierachy

We derive the determinant representation and Hirota equations for the regularized correlation functions of the light-like coordinate operators $\sim \prod_{i} {\Tr}(X^{+})^{l_{i}}$ in the reductions to zero dimensions of the matrix models describing $D$-particles in various dimensions. We investigate in great detail the matrix model originally proposed by J. Hoppe and recently encountered in studies of $D$-particles in four dimensions. We also present a new derivation of the large $N$ and double scaling limits of the one-matrix model with cubic potential.