Proof Methods in Random Matrix Theory
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.02551
- arXiv:
- arXiv:2203.02551
- Bibcode:
- 2022arXiv220302551F
- Keywords:
-
- Mathematics - Probability