Meixner matrix ensembles
Wlodek Bryc, Gerard Letac

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.
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Taxonomy
TopicsRandom Matrices and Applications · Matrix Theory and Algorithms · Advanced Combinatorial Mathematics
