GENERAL BEHAVIOR OF THE QUENCHED AVERAGED SPECTRAL DENSITY WITH A CHANGE IN THE ENSEMBLE PROBABILITY-DISTRIBUTION

The behavior of the ensemble-averaged spectral density [G(z)] for a given eigenvalue problem (zdelta(ij)-PHI(ij))y(j) = 0 with the random matrix PHI, distributed by the probability P(PHI), will be examined. By using the replica method, the change of [G(z)] for an infinitesimal neighboring distribution is calculated and, as a result, it was found that for systems with a higher disorders of the random matrix PHI the averaged spectral density increases for very small and very large values of z, respectively.