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For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure.
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Pastur, L. and Shcherbina, M. (2011). Eigenvalue distribution of large random matrices. Mathematical Surveys and Monographs
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Chatterjee, S. (2006). A generalization of the Lindeberg principle. Ann. Probab
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