论文标题
来自单一和正交组的随机矩阵的换向器
Commutators of random matrices from the unitary and orthogonal groups
论文作者
论文摘要
我们研究$ c = uvu^{ - 1} v^{ - 1} $的统计属性，当$ u $和$ v $是独立的随机矩阵时，就$ u（n）$ u（n）$和$ o（n）$的HAAR度量均匀分布。对于$ c $的功率和对称函数的平均值，以及与$ c $的矩阵元素的产品，类似于Weingarten函数的矩阵元素的产品。 $ c $的特征值的密度显示在很大的$ n $限制中变得恒定，并且找到了第一个$ n^{ - 1} $校正。
We investigate the statistical properties of $C=uvu^{-1}v^{-1}$, when $u$ and $v$ are independent random matrices, uniformly distributed with respect to the Haar measure of the groups $U(N)$ and $O(N)$. An exact formula is derived for the average value of power sum symmetric functions of $C$, and also for products of the matrix elements of $C$, similar to Weingarten functions. The density of eigenvalues of $C$ is shown to become constant in the large-$N$ limit, and the first $N^{-1}$ correction is found.
