Free infinite divisibility for beta distributions and related ones

Abstract

We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, ultraspherical and many of Student t-distributions have free divisibility indicator 1.

37 pages, 6 figures, slightly different from the published version

References in corpus (7)

• On the Law of Free Subordinators
• Classical and free infinitely divisible distributions and random matrices
• A class of multivariate infinitely divisible distributions related to arcsine density
• On generalized Cauchy-Stieltjes transforms of some Beta distributions
• On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws
• On free infinite divisibility for classical Meixner distributions
• The sector constants of continuous state branching processes with immigration

Cited by in corpus (5)

• Classical Scale Mixtures of Boolean Stable Laws
• Limit theorems for free Lévy processes
• Extreme matrices or how an exponential map links classical and free extreme laws
• On freely quasi-infinitely divisible distributions
• Free infinite divisibility for generalized power distributions with free Poisson term