Gaussian representation of a class of Riesz probabilitydistributions

TL;DR

This paper demonstrates that certain Riesz probability distributions, extending the Wishart distribution, can be represented using Gaussian samples with missing data, linking harmonic analysis and matrix distributions.

Contribution

It introduces a Gaussian representation for a class of Riesz distributions, broadening the understanding of their structure beyond Wishart distributions.

Findings

Riesz distributions can be expressed via Gaussian samples with missing data

The representation generalizes the Wishart distribution

Harmonic analysis techniques underpin the new representation

Abstract

The Wishart probability distribution on symmetricmatrices has been initially defined by mean of the multivariateGaussian distribution as an of the chi-square distribution. A moregeneral definition is given using results for harmonic analysis.Recently a probability distribution on symmetric matrices called theRiesz distribution has been defined by its Laplace transform as ageneralization of the Wishart distribution. The aim of the presentpaper is to show that some Riesz probability distributions which arenot necessarily Wishart may also be presented by mean of theGaussian distribution using Gaussian samples with missing data.