On the Limiting Spectral Density of Symmetric Random Matrices with Correlated Entries
Conference paper
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Abstract
We analyze the spectral distribution of two different models of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation the limiting spectral distribution is either the famous semicircle law known for the limiting spectral density of symmetric random matrices with independent entries, or some other law related to that derived for Toeplitz matrices by Bryc W, Dembo A, Jiang T (2006) Spectral measure of large random Hankel, Markov and Toeplitz matrices. Ann Probab 34(1):1–38.
Keywords
Random Matrice Spectral Distribution Toeplitz Matrice Independent Copy Gaussian Markov Process
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