High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices

We study the high-dimensional asymptotic regimes of correlated Wishart matrices [Formula: see text], where text] is a Gaussian random matrix with and non-stationary entries. prove that under different normalizations, two distinct emerge as both grow to infinity. The first regime one central convergence, law properly renormalized becomes close in Wasserstein distance orthogonal ensemble matrix. In second regime, non-central convergence happens, normalized so-called Rosenblatt–Wishart recently introduced by Nourdin Zheng. then proceed show convergences stated above also hold functional setting, namely weak text]. As an application our main result (in regime), we it can be used expectation empirical spectral distributions semicircular law. Our findings complement extend rich collection results on fluctuations matrices, provide explicit examples based entries given increments bi-fractional or sub-fractional Brownian motion.