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arXiv · 1004.4717

General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Sho Matsumoto
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Abstract

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.

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Sho Matsumoto. 2011-02-21. General moments of the inverse real Wishart distribution and orthogonal Weingarten functions. https://doi.org/10.1007/s10959-011-0340-0

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