Regression conditions that characterize free-Poisson and free-Kummer distributions
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Published:2021-07-31
Issue:
Volume:
Page:2250019
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ISSN:2010-3263
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Container-title:Random Matrices: Theory and Applications
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language:en
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Short-container-title:Random Matrices: Theory Appl.
Affiliation:
1. Warsaw University of Technology, Address, Warsaw 00-661, Poland
Abstract
We find the asymptotic spectral distribution of random Kummer matrix. Then we formulate and prove a free analogue of HV independence property, which is known for classical Kummer and Gamma random variables and for Kummer and Wishart matrices. We also prove a related characterization of free-Kummer and free-Poisson (Marchenko–Pastur) non-commutative random variables.
Funder
Narodowym Centrum Nauki
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory