95-8 Khorunzhy A., Khoruzhenko B., Pastur L.
ON THE $1/N$ CORRECTIONS TO THE GREEN FUNCTIONS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES (19K, TEX) Jan 9, 95
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We propose a general approach to the construction of $1/N$ corrections to the Green function $G_N(z)$ of the ensembles of random real symmetric and Hermitean $N \times N$ matrices with independent entries $H_{k,l}$. By this approach we study the correlation function $C_N(z_1,z_2)$ of normalized trace $N^{-1}\mbox{Tr}\;G_N$ assuming that the average of $|H_{k,l}|^5$ is bounded. We found that to the leading order $C_N(z_1,z_2)=N^{-2}F(z_1,z_2)$, 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

Files: 95-8.tex