  We consider a Hamiltonian $H$ which is the sum of a deterministic part $H_0$
and of a random potential $V$. For finite $N \times N$ matrices, following a
method introduced by Kazakov, we derive a representation of the correlation
functions in terms of contour integrals over a finite number of variables. This
allows one to analyse the level correlations, whereas the standard methods of
random matrix theory, such as the method of orthogonal polynomials, are not
available for such cases. At short distance we recover, for an arbitrary $H_0$,
an oscillating behavior for the connected two-level correlation.
