  It has been observed that the statistical distribution of the eigenvalues of
random matrices possesses universal properties, independent of the probability
law of the stochastic matrix. In this article we find the correlation functions
of this distribution in two classes of random hermitian matrix models: the
one-matrix model, and the two-matrix model, although it seems that the methods
and conclusions presented here will allow generalization to other multi-matrix
models such as the chain of matrices, or the O(n) model. We recover the
universality of the two point function in two regimes: short distance regime
when the two eigenvalues are separated by a small number of other eigenvalues,
and on the other hand the long range regime, when the two eigenvalues are far
away in the spectrum, in this regime we have to smooth the short scale
oscillations. We also discuss the universality properties of more than two
eigenvalues correlation functions.
