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Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices

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Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices
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17
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In this talk, we will consider high-dimensional Wishart matrices associated with a rectangular random matrix X_{n,d) whose entries are jointly Gaussian and correlated. Our main focus will be on the case where the rows of X_{n,d) are independent copies of a n-dimensional stationary centered Gaussian vector of correlation function s. When s is 4/3-integrable, we will show that a proper normalization of the corresponding Wishart matrix is close in Wasserstein distance to the corresponding Gaussian ensemble as long as d is much larger than n3, thus recovering the main finding of Bubeck et al. and extending it to a larger class of matrices.