On free infinite divisibility for classical Meixner distributions

Abstract

We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\Gamma (t+ix){|}^2$, are freely infinitely divisible for $0<t\le \frac{1}{2}$. The case $t=\frac{1}{2}$ corresponds to the law of Lévy'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.

12 pages

References in corpus (2)

• On the Law of Free Subordinators
• Classical and free infinite divisibility for Boolean stable laws

Cited by in corpus (5)

• Fock space associated to Coxeter group of type B
• Free infinite divisibility for beta distributions and related ones
• Classical Scale Mixtures of Boolean Stable Laws
• On freely quasi-infinitely divisible distributions
• Free infinite divisibility for powers of random variables