Tracy-Widom F_2分布的普适性(英文)

The Universality of Tracy-Widom F_2 Distribution

随机矩阵理论与数学和物理中各种其他领域相联系,而与随机矩阵特征值相关的分布函数发挥着重要的作用.这篇综述主要讨论一个著名的具有普适性的分布—Tacy-WidomF2分布,它是高斯幺正系综随机矩阵最大特征值的极限分布.为了描绘它的普适性,本文列出了数学和物理中的某些模型.读者同样能看到关于这些具体模型的一些近来的结果和它们之间的关系以及研究它们的常用方法和技巧,特别是RSK对应性.

It has been shown that random matrix theory is connected with various other domains of mathematics and physics, where the distribution functions related to eigenvalues of random matrices play a key role. In this survey, we focus on a celebrated universal law-Tracy- Widom F2 distribution which is the limit distribution of the largest eigenvalue of Gaussian unitary ensemble（GUE）. Some certain models in mathematics and physics are also reviewed to show its universality. Readers will also find some recent results and their associations as well as some commonly used methods and techniques especially the RSK correspondence in studying those specific models.