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

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.

29 pages. The last version differs from the published version, but it includes Appendix

References in corpus (3)

• On some properties of orthogonal Weingarten functions
• Jucys-Murphy elements and Weingarten matrices
• Graph presentations for moments of noncentral Wishart distributions and their applications

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