Multiplicative free square of the free Poisson measure and examples of free symmetrization
Volume 119 / 2010
Colloquium Mathematicum 119 (2010), 127-136
MSC: Primary 46L54; Secondary 44A60, 60C05.
DOI: 10.4064/cm119-1-8
Abstract
We compute the moments and free cumulants of the measure $\rho_t:=\pi_t\mathbin{{\scriptstyle\boxtimes}}\pi_t$, where $\pi_t$ denotes the free Poisson law with parameter $t>0$. We also compute free cumulants of the symmetrization of $\rho_t$. Finally, we introduce the free symmetrization of a probability measure on $\mathbb{R}$ and provide some examples.
