TL;DR
This paper introduces a random matrix model for free Meixner laws using matricial freeness, extending the understanding of asymptotic joint distributions and conditional freeness in Gaussian random matrices.
Contribution
It develops a natural framework for modeling free Meixner laws with random matrices, generalizing previous results on asymptotic freeness.
Findings
Constructs a random matrix model for free Meixner laws.
Shows asymptotic conditional freeness of the ensemble.
Provides a block refinement of Voiculescu's asymptotic freeness result.
Abstract
Applying the concept of matricial freeness which generalizes freeness in free probability, we have recently studied asymptotic joint distributions of symmetric blocks of Gaussian random matrices (Gaussian Symmetric Block Ensemble). This approach gives a block refinement of the fundamental result of Voiculescu on asymptotic freeness of independent Gaussian random matrices. In this paper, we show that this framework is natural for constructing a random matrix model for free Meixner laws. We also demonstrate that the ensemble of independent matrices of this type is asymptotically conditionally free with respect to the pair of partial traces.
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