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.
Acknowledgments
We are grateful for the very detailed feedback from the referee and the associate editor, which helped improve this paper in many places.
Citation
Michael Fleermann. Werner Kirsch. "Proof methods in random matrix theory." Probab. Surveys 20 291 - 381, 2023. https://doi.org/10.1214/23-PS16
Information
