Multiplicative free square of the free Poisson measure and examples of free symmetrization
Tom 119 / 2010
Colloquium Mathematicum 119 (2010), 127-136
MSC: Primary 46L54; Secondary 44A60, 60C05.
DOI: 10.4064/cm119-1-8
Streszczenie
We compute the moments and free cumulants of the measure , 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.