BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices Nourdin, Ivan


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 $n^3$, thus recovering the main finding of Bubeck et al. and extending it to a larger class of matrices.

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