Meixner matrix ensembles

TL;DR

This paper constructs and analyzes a family of matrix ensembles called Meixner matrix ensembles, solving their Laplace transforms and classifying the 2x2 cases, advancing understanding of matrix-valued probability laws.

Contribution

It introduces a new family of matrix ensembles fitting specific regression postulates and explicitly solves their Laplace transforms for 2x2 cases, identifying six types.

Findings

Laplace transform satisfies a solvable PDE system for n=2

Explicit classification of six 2x2 Meixner matrix ensembles

Provides a framework for matrix-valued Meixner laws

Abstract

We construct a family of matrix ensembles that fits Anshelevich's regression postulates for "Meixner laws on matrices". We show that the Laplace transform of a general n by n Meixner matrix ensemble satisfies a system of partial differential equations which is explicitly solvable for n=2. We rely on these solutions to identify the six types of 2 by 2 Meixner matrix ensembles.