Proof Methods in Random Matrix Theory
Probability
2022-03-08 v1
Abstract
In this survey article, we give an introduction to two methods of proof in random matrix theory: The method of moments and the Stieltjes transform method. We thoroughly develop these methods and apply them to show both the semicircle law and the Marchenko-Pastur law for random matrices with independent entries. The material is presented in a pedagogical manner and is suitable for anyone who has followed a course in measure-theoretic probability theory.
Keywords
Cite
@article{arxiv.2203.02551,
title = {Proof Methods in Random Matrix Theory},
author = {Michael Fleermann and Werner Kirsch},
journal= {arXiv preprint arXiv:2203.02551},
year = {2022}
}