  We consider a Gaussian random matrix theory in the presence of an external
matrix source. This matrix model, after duality (a simple version of the
closed/open string duality), yields a generalized Kontsevich model through an
appropriate tuning of the external source. The n-point correlation functions of
this theory are shown to provide the intersection numbers of the moduli space
of curves with a p-spin structure, n marked points and top Chern class. This
sheds some light on Witten's conjecture on the relationship with the pth-KdV
equation.
