We have discussed earlier the correlation functions of the random variables det(lambda-X) in which X is a random matrix. In particular, the moments of the distribution of these random variables are universal functions, when measured in the appropriate units of the level spacing. When the lambda's, instead of belonging to the bulk of the spectrum, approach… (More)

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 H0 and of a random potential φ. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed H0 and for a class of probability… (More)

Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous work to the case in which the random matrix evolves in time or varies as some external parameters vary. We compute the… (More)