Abstract

We propose a general approach to the construction of 1=N corrections to the Green function GN (z) of the ensembles of random real symmetric and Hermitean N \Theta N matrices with independent entries H k;l . By this approach we study the correlation function CN (z 1 ; z 2 ) of normalized trace N \Gamma1 Tr GN assuming that the average of jH k;l j 5 is bounded. We found that to the leading order CN (z 1 ; z 2 ) = N \Gamma2 F (z 1 ; z 2 ), where F (z 1 ; z 2 ) depends only on the second and the fourth moments of H k;l . For the correlation function of the density of energy levels we obtain an expression which, in the scaling limit depends only on the second moment of H k;l . This can be viewed as a support to the universality conjecture of random matrix theory 1. Random N \Theta N matrices with independent entries were introduced by E.Wigner [1]. The majority of rigorous results for these matrices concerns the proof of convergence of the density ae N (E) of their eigenvalues to t...

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