RM+ML: 21. Another Proof of Marchenko-Pastur -- Via Stein's Identity

The lecture notes for the course can be found at https://rolandspeicher.com/wp-content... Stein's identity, resolvent, proof of Marchenko-Pastur 0:00 Motivation 2:13 Idea of proof of MP 12:38 Stein's identity 24:28 Finishing the proof of MP The goal of this lecture series is to cover mathematical interesting aspects of neural networks, in particular, those related to random matrices. In this 21th lecture we prepare the proof of our theorem on the asymptotic eigenvalue distribution in the random feature model, by giving another proof of the Marchenko-Pastur law. This new approach relies on partial integration for the Gauss distribution, aka Stein's identity. This has the advantage that in the next lecture we can generalize this approach to non-Gaussian and non-independent situations, which will allow us to deal with the random feature model.