  Kontsevich's work on Airy matrix integrals has led to explicit results for
the intersection numbers of the moduli space of curves. In this article we show
that a duality between k-point functions on $N\times N$ matrices and N-point
functions of $k\times k$ matrices, plus the replica method, familiar in the
theory of disordered systems, allows one to recover Kontsevich's results on the
intersection numbers, and to generalize them to other models. This provides an
alternative and simple way to compute intersection numbers with one marked
point, and leads also to some new results.
