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A Simple Formula for the Moments of Unitarily Invariant Matrix Distributions | IEEE Conference Publication | IEEE Xplore

A Simple Formula for the Moments of Unitarily Invariant Matrix Distributions


Abstract:

We present a new formula for computing arbitrary moments of unitarily invariant matrix distributions. The Schur-Weyl duality is used to decompose the expected value of te...Show More

Abstract:

We present a new formula for computing arbitrary moments of unitarily invariant matrix distributions. The Schur-Weyl duality is used to decompose the expected value of tensor powers of the random matrices as a linear combination of projection operators onto unitary irreducible representations. The coefficients in this combination, which are labeled by Young diagrams, are expectations of products of determinants of the random matrices. It is demonstrated in a number of important cases, including matrix gamma and matrix beta distributions, that these coefficients can be simply computed from a knowledge of the normalization factors of the distributions.
Date of Conference: 23-27 May 2022
Date Added to IEEE Xplore: 27 April 2022
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Conference Location: Singapore, Singapore

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