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

Volume 119 / 2010

Melanie Hinz, Wojciech Młotkowski 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.

Authors

  • Melanie HinzMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Wojciech MłotkowskiMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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