Stein方法与紧李群的特征
Stein's Method and Characters of Compact Lie Groups
摘要：
Stein方法用于研究紧致李群或对称空间中随机元的迹。中心极限定理证明使用非常少的信息：字符值的一个单一的元素和分解的平方的痕迹成不可约的组成部分。这说明了李群的经典类型和戴森的圆形合奏。本文的方法对于高维特征的研究将是有用的，在高维特征中，正规近似不需要成立。
英文摘要：
Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson's circular ensembles. The approach in this paper will be useful for the study of higher dimensional characters, where normal approximations need not hold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
