Free powers of the free Poisson measure
Volume 123 / 2011
Colloquium Mathematicum 123 (2011), 285-290
MSC: Primary 46L54; Secondary 44A60, 60C05.
DOI: 10.4064/cm123-2-11
Abstract
We compute moments of the measures $(\mathbf{\varpi}^{\boxtimes p})^{\boxplus t}$, where $\varpi$ denotes the free Poisson law, and $\boxplus$ and $\boxtimes$ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss–Narayana numbers.
