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Free powers of the free Poisson measure

Melanie Hinz; Wojciech Młotkowski — 2011

Colloquium Mathematicae

We compute moments of the measures ${(ϖ^{⊠ p})}^{⊞ t}$ , where ϖ denotes the free Poisson law, and ⊞ and ⊠ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss-Narayana numbers.

Multiplicative free square of the free Poisson measure and examples of free symmetrization

Melanie Hinz; Wojciech Młotkowski — 2010

Colloquium Mathematicae

We compute the moments and free cumulants of the measure $ρ_{t} : = π_{t} ⊠ π_{t}$ , where $π_{t}$ denotes the free Poisson law with parameter t > 0. We also compute free cumulants of the symmetrization of $ρ_{t}$ . Finally, we introduce the free symmetrization of a probability measure on ℝ and provide some examples.

Free cumulants of some probability measures

Melanie Hinz; Wojciech Młotkowski — 2007

Banach Center Publications

Limit Measures Related to the Conditionally Free Convolution

Melanie Hinz; Wojciech Młotkowski — 2008

Bulletin of the Polish Academy of Sciences. Mathematics

We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.

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