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• W2078757002 abstract "We study the normalized trace $g_n(z)=n^{-1} mbox{tr} , (H-zI)^{-1}$ of the resolvent of $ntimes n$ real symmetric matrices $H=big[(1+delta_{jk})W_{jk}/sqrt nbig]_{j,k=1}^n$ assuming that their entries are independent but not necessarily identically distributed random variables. We develop a rigorous method of asymptotic analysis of moments of $g_n(z)$ for $|Im z| ge eta_0$ where $eta_0$ is determined by the second moment of $W_{jk}$. By using this method we find the asymptotic form of the expectation ${bf E}{g_n(z)}$ and of the connected correlator ${bf E}{g_n(z_1)g_n(z_2)}- {bf E}{g_n(z_1)} {bf E}{g_n(z_2)}$. We also prove that the centralized trace $ng_n(z)- {bf E}{ng_n(z)}$ has the Gaussian distribution in the limit $n=infty $. Basing on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles." @default.
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• W2078757002 date "1996-10-01" @default.
• W2078757002 modified "2023-10-06" @default.
• W2078757002 title "Asymptotic properties of large random matrices with independent entries" @default.
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• W2078757002 doi "https://doi.org/10.1063/1.531589" @default.
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