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Regression conditions that characterizes free--Poisson and free--Kummer distributions

Published 5 Jul 2019 in math.OA and math.PR | (1907.02826v3)

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.

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