随机矩阵理论中的证明方法

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2022-03-04 DOI:10.1214/23-ps16

Michael Fleermann, W. Kirsch

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引用次数: 2

摘要

本文简要介绍了随机矩阵理论中的两种证明方法:矩量法和Stieltjes变换法。我们深入地发展了这些方法，并应用它们来证明具有独立项的随机矩阵的半圆定律和Marchenko-Pastur定律。材料以教学的方式呈现，适合任何参加过测量论概率论课程的人。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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