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MacMahon's Master Theorem, Representation Theory, and Moments of Wishart Distributions

✍ Scribed by I-Li Lu; Donald St.P. Richards

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 173 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0748

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✦ Synopsis

independently derived a generalization of MacMahon's master theorem. In this article we apply their result to obtain an explicit formula for the moments of arbitrary polynomials in the entries of X, a real random matrix having a Wishart distribution. In the case of the complex Wishart distributions, the same method is applicable. Furthermore, we apply the representation theory of GL d , the complex general linear group, to derive explicit formulas for the expectation of Kronecker products of any complex Wishart random matrix.

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