An explicit Wishart moment formula for the product of two disjoint principal minors

Genest, Christian; Ouimet, Frédéric; Richards, Donald

doi:10.1090/proc/17077

An explicit Wishart moment formula for the product of two disjoint principal minors
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by Christian Genest, Frédéric Ouimet and Donald Richards;

Proc. Amer. Math. Soc. 153 (2025), 1299-1311

DOI: https://doi.org/10.1090/proc/17077

Published electronically: December 12, 2024

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Abstract:

This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks [Ann. of Math. (2) 35 (1934), pp. 312–340]. The proof makes crucial use of hypergeometric functions of matrix argument and their Laplace transforms. Additionally, a Wishart generalization of the Gaussian product inequality conjecture is formulated and a stronger quantitative version is proved to hold in the case of two minors.

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