Proof methods in random matrix theory
Copyright policy )Proof methods in random matrix theory
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.
- University of Hagen Germany
Random matrices (probabilistic aspects), Stieltjes transform method, Marchenko-Pastur law, method of moments, empirical spectral distributions, Probability (math.PR), FOS: Mathematics, random matrix theory, Research exposition (monographs, survey articles) pertaining to probability theory, semicircle law, Mathematics - Probability
Random matrices (probabilistic aspects), Stieltjes transform method, Marchenko-Pastur law, method of moments, empirical spectral distributions, Probability (math.PR), FOS: Mathematics, random matrix theory, Research exposition (monographs, survey articles) pertaining to probability theory, semicircle law, Mathematics - Probability
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