General Moments of the Inverse Real Wishart Distribution and Orthogonal Weingarten Functions
General Moments of the Inverse Real Wishart Distribution and Orthogonal Weingarten Functions
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DOI：
10.1007/s10959-011-0340-0
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发表时间：
2010-04
影响因子：
0.8
通讯作者：
Sho Matsumoto
中科院分区：
文献类型：
--
作者：
Sho Matsumoto
我们研究根据实数 Wishart 分布分布的随机正定对称矩阵。我们显式地计算随机矩阵及其逆矩阵的一般矩。为此，我们采用了正交 Weingarten 函数，该函数是最近在 Haar 分布正交矩阵的研究中引入的。作为应用，我们给出了 Wishart 矩阵及其逆矩阵的迹矩的公式。
We study a random positive definite symmetric matrix distributed according to a real Wishart distribution. We compute general moments of the random matrix and of its inverse explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study of Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.