- 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
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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
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