Universal correlations for deterministic plus random Hamiltonians

We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic ${\mathit{H}}_0$, and of a random potential cphi. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed ${\mathit{H}}_0$ and for a class of probability distribution P(cphi) of the random potential. We find a compact representation of the correlation function. From this representation one readily obtains the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both ${\mathit{H}}_0$ and P(cphi).