论文标题
自由概率的方法
Methods of free probability
论文作者
论文摘要
这是对经典和自由概率的联合介绍，即双姐妹。我们首先回顾了经典概率的基础，尤其是主要限制定理（CLT，CCLT，PLT，CPLT），并查看来自Lie组和随机矩阵的示例。然后，我们提出了自由概率的基础和主要结果，特别是具有自由限制定理，并查看来自量子组和随机矩阵的示例。然后，我们讨论了许多更高级的方面，与自由几何学和亚比例理论有关。
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples coming from Lie groups and random matrices. Then we present the foundations and main results of free probability, notably with free limiting theorems, and with a look into examples coming from quantum groups and random matrices. We discuss then a number of more advanced aspects, in relation with free geometry and with subfactor theory.
