Geodesic
Multiplicative free square of the free Poisson measure and examples of free symmetrization
Melanie Hinz1 ; Wojciech Młotkowski1
1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 127-136.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_cm119_1_8,
     author = {Melanie Hinz and Wojciech M{\l}otkowski},
     title = {Multiplicative free square of the free {Poisson} measure
and examples of free symmetrization},
     journal = {Colloquium Mathematicum},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {119},
     number = {1},
     year = {2010},
     doi = {10.4064/cm119-1-8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm119-1-8/}
}
TY  - JOUR
AU  - Melanie Hinz
AU  - Wojciech Młotkowski
TI  - Multiplicative free square of the free Poisson measure
and examples of free symmetrization
JO  - Colloquium Mathematicum
PY  - 2010
SP  - 127
EP  - 136
VL  - 119
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm119-1-8/
DO  - 10.4064/cm119-1-8
LA  - en
ID  - 10_4064_cm119_1_8
ER  - 
%0 Journal Article
%A Melanie Hinz
%A Wojciech Młotkowski
%T Multiplicative free square of the free Poisson measure
and examples of free symmetrization
%J Colloquium Mathematicum
%D 2010
%P 127-136
%V 119
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm119-1-8/
%R 10.4064/cm119-1-8
%G en
%F 10_4064_cm119_1_8
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. http://geodesic.mathdoc.fr/articles/10.4064/cm119-1-8/

Cité par Sources :