Geodesic
Multiplicative free square of the free Poisson measure and examples of free symmetrization
Melanie Hinz 1   ; Wojciech Młotkowski 1
1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 127-136 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm119-1-8
Keywords: compute moments cumulants measure rho mathbin scriptstyle boxtimes where denotes poisson law parameter compute cumulants symmetrization rho finally introduce symmetrization probability measure mathbb provide examples

Melanie Hinz  1   ; Wojciech Młotkowski  1

1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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Melanie Hinz; Wojciech Młotkowski. Multiplicative free square of the free Poisson measure
and examples of free symmetrization. Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 127-136. doi: 10.4064/cm119-1-8

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