On the Lukacs property for free random variables
Kamil Szpojankowski (2015)
Studia Mathematica
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The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and are free. As an auxiliary result we compute the joint cumulants of and for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.