• Corpus ID: 55878358

On free infinite divisibility for classical Meixner distributions

@article{Boejko2013OnFI,
  title={On free infinite divisibility for classical Meixner distributions},
  author={Marek Bożejko and Takahiro Hasebe},
  journal={arXiv: Probability},
  year={2013}
}

• M. Bożejko, Takahiro Hasebe
• Published 20 February 2013
• Mathematics
• arXiv: Probability

We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\Gamma(t+ix)|^2$, are freely infinitely divisible for $0<t\leq\frac{1}{2}$. The case $t=\frac{1}{2}$ corresponds to the law of L\'evy's stochastic area whose probability density is $\frac{1}{\cosh(\pi x)}$. A logistic distribution, whose probability density is proportional to $\frac{1}{\cosh^2(\pi x)}$, is freely infinitely divisible too.