Alexander Aue : Random matrix theory for high-dimensional time series

In this talk, I will discuss how the fundamental Marcenko-Pastur (MP) theorem may be extended to high-dimensional linear processes satisfying certain assumptions. The MP theorem describes the limiting behavior of the eigenvalues of the sample covariance matrix in the independent case. Understanding the behavior of the eigenvalues of the sample covariance matrix under temporal dependence is important from an applied point of view and challenging from a theoretical perspective. The talk will mostly focus on intuition and intersperse theory only if needed.