Free infinite divisibility and free multiplicative mixtures of the Wigner distribution
Victor Perez-Abreu, Noriyoshi Sakuma
TL;DR
This paper establishes conditions for free additive infinite divisibility of certain free multiplicative convolutions involving distributions like Wigner, arcsine, and free Poisson, with explicit examples provided.
Contribution
It provides necessary and sufficient criteria for free additive infinite divisibility of specific free multiplicative convolutions, expanding understanding of these distributions.
Findings
Conditions for free additive infinite divisibility are characterized.
Explicit examples illustrate the theoretical results.
Results apply to Wigner, arcsine, and free Poisson distributions.
Abstract
We find necessary and sufficient conditions for the free additive infinite divisibility of some free multiplicative convolutions with the Wigner, the arcsine, the free Poisson and other distributions, including explicit examples.
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Taxonomy
TopicsRandom Matrices and Applications · Bayesian Methods and Mixture Models · Advanced Algebra and Geometry