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Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Probability theory and stochastic processes; Partial differential equations

video/mp4

Author affiliation: University of Luxembourg

2019-03-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69078

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/