ON THE 1 N CORRECTIONS TO THE GREEN-FUNCTIONS OF RANDOM MATRICES WITHINDEPENDENT ENTRIES/

We propose a general approach to the construction of 1/N corrections t o the Green function G(N)(z) Of the ensembles of random real-symmetric and Hermitian N x N matrices with independent entries H-k,H-l. By thi s approach we study the correlation function C-N(z(1),z(2)) of the nor malized trace N(-1)Tr G(N) assuming that the average of \H-k,H-l\(5) i s bounded. We found that to the leading order C-N(z(1),z(2)) = N-2F(z( 1),z(2)) where F(z(1),z(2)) only depends on the second and the fourth moments of H-k,H-l. For the correlation function of the density of ene rgy levels we obtain an expression which, in the scaling limit only de pends on the second moment of H-k,H-l. This can be viewed as supportin g the universality conjecture of random matrix theory.