Modern Aspects of Random Matrix Theory
Modern Aspects of Random Matrix Theory
复制标题
随机矩阵理论的现代方面
DOI：
10.1090/psapm/072
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
V. Vu
中科院分区：
文献类型：
--
作者：
V. Vu
随机矩阵理论是数学中一个非常丰富的话题。随机矩阵在统计学、数学物理、组合学、理论计算机科学、数论和数值分析等各个领域发挥着重要作用。本卷是基于2013年1月6日至7日在加利福尼亚州圣地亚哥举行的AMS随机矩阵短期课程的讲座。其中包括由该领域的主要研究人员进行的调查，以介绍性风格撰写，旨在为读者提供这个迷人且快速发展的主题的快速直观概述。这些调查包含了许多重要的最新发展，如普世性猜想的进展，随机矩阵和自由概率之间的联系，数值代数，组合学和高维几何，以及一些新方法和各种开放问题。
The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6-7, 2013 in San Diego, California. Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions.