论文标题
关于“随机矩阵”的讲义
Lecture Notes on "Random Matrices"
论文作者
论文摘要
这在对随机矩阵理论的介绍中，给人留下了现代主题的一些最重要方面的印象。特别是，它涵盖了围绕Wigner的半圆定律的基本组合和分析理论，其中还具有浓度现象，以及最大的特征值的Tracy-Widom分布。循环定律和对voiculescu的半圆定律的多元扩展的讨论，作为自由概率理论的开胃菜，也出现了。 这里的材料在2019/20冬季在萨尔兰大学（Saarland University）提供了24分钟的讲座，为90分钟。记录了讲座，可以在https://www.math.uni-sb.de/ag/speicher/web_video/index.html上在线找到。
This in an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigner's semicircle law, featuring also concentration phenomena, and the Tracy-Widom distribution of the largest eigenvalue. The circular law and a discussion of Voiculescu's multivariate extension of the semicircle law, as an appetizer for free probability theory, also make an appearance. The material here was presented in the winter term 2019/20 at Saarland University in 24 lectures of 90 minutes each. The lectures were recorded and can be found online at https://www.math.uni-sb.de/ag/speicher/web_video/index.html.
