Proof Methods in Random Matrix Theory

Michael Fleermann; Werner Kirsch

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arXiv · 2203.02551

Proof Methods in Random Matrix Theory

Michael Fleermann·Werner Kirsch

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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.

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Michael Fleermann, Werner Kirsch. 2022-03-04. Proof Methods in Random Matrix Theory. https://arxiv.org/abs/2203.02551

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