TY - JOUR

T1 - MacMahon's master theorem, representation theory, and moments of Wishart distributions

AU - Lu, I. Li

AU - Richards, Donald St P.

N1 - Funding Information:
1Research supported in part by a grant to the Institute for Advanced Study from the Bell Fund and by the National Science Foundation under Grant DMS-9703705.

PY - 2001

Y1 - 2001

N2 - D. Foata and D. Zeilberger (1988, SIAM J. Discrete Math. 4, 425-433) and D. Vere-Jones (1988, Linear Algebra Appl. 111, 119-124) 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, ℂ), the complex general linear group, to derive explicit formulas for the expectation of Kronecker products of any complex Wishart random matrix.

AB - D. Foata and D. Zeilberger (1988, SIAM J. Discrete Math. 4, 425-433) and D. Vere-Jones (1988, Linear Algebra Appl. 111, 119-124) 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, ℂ), 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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U2 - 10.1006/aama.2001.0748

DO - 10.1006/aama.2001.0748

M3 - Article

AN - SCOPUS:0035428978

SN - 0196-8858

VL - 27

SP - 531

EP - 547

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 2-3

ER -