Olle Englund: An approximate version of the Marchenko–Pastur equation

Abstract.

The Marchenko–Pastur equation is one of the fundamental results of random matrix theory. Via the Stieltjes transform, the equation describes the behaviour of the eigenvalues of certain random matrices as the dimension of the matrices tends to infinity. In this presentation we give an overview of a proof of an approximate version of the Marchenko–Pastur equation. Furthermore, we take a look at the approximate equation without its error term, and mention some of its properties.