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

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.

21 pages, 2 figures

References in corpus (3)

• On a class of free Levy laws related to a regression problem
• Change of measure technique in characterizations of the Gamma and Kummer distributions
• Kummer and gamma laws through independences on trees - another parallel with the Matsumoto-Yor property