On the Moments of Traces of Matrices of Classical Groups
On the Moments of Traces of Matrices of Classical Groups
复制标题
论经典群矩阵迹的矩
DOI：
10.1007/s00220-004-1231-3
复制
发表时间：
2004
影响因子：
2.4
通讯作者：
V. Vasilchuk
中科院分区：
文献类型：
--
作者：
L. Pastur;V. Vasilchuk
我们考虑U(n)， O(n)， SO(n), Sp(n)群的随机矩阵，并根据相应的单位Haar测度进行分布。证明了在矩阶足够低的情况下，矩阵幂迹的矩与某些高斯随机变量的矩重合。以前用各种方法部分证明过的相应公式，在这里用一种独特的方法得到，使人联想到统计力学中相关方程的方法。这些方程是用分部积分法的一种形式推导出来的。
We consider random matrices, belonging to the groups U(n), O(n) , SO(n), and Sp(n) and distributed according to the corresponding unit Haar measure. We prove that the moments of traces of powers of the matrices coincide with the moments of certain Gaussian random variables if the order of moments is low enough. Corresponding formulas, proved partly before by various methods, are obtained here in the framework of a unique method, reminiscent of the method of correlation equations of statistical mechanics. The equations are derived by using a version of the integration by parts.