Multiplicative free square of the free Poisson measure and examples of free symmetrization

Melanie Hinz; Wojciech Młotkowski

Colloquium Mathematicae, Tome 120 (2010), p. 127-136 / Harvested from The Polish Digital Mathematics Library

Résumé

We compute the moments and free cumulants of the measure $ρ_{t} : = π_{t} ⊠ π_{t}$ , where $π_{t}$ denotes the free Poisson law with parameter t > 0. We also compute free cumulants of the symmetrization of $ρ_{t}$ . Finally, we introduce the free symmetrization of a probability measure on ℝ and provide some examples.

Publié le : 2010-01-01

Zbl 1197.46036

EUDML-ID : urn:eudml:doc:283804

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     author = {Melanie Hinz and Wojciech M\l otkowski},
     title = {Multiplicative free square of the free Poisson measure and examples of free symmetrization},
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {127-136},
     zbl = {1197.46036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-8}
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Melanie Hinz; Wojciech Młotkowski. Multiplicative free square of the free Poisson measure and examples of free symmetrization. Colloquium Mathematicae, Tome 120 (2010) pp. 127-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-8/