Free Infinite Divisibility for Q-gaussians
نویسنده
چکیده
We prove that the q-Gaussian distribution is freely infinitely divisible for all q ∈ [0, 1].
منابع مشابه
Lévy processes on a first order model
The classical notion of a Lévy process is generalized to one that takes values in an arbitrary model of a first order language. This is achieved by defining a convolution product and the infinite divisibility with respect to it.
متن کاملFree infinite divisibility for beta distributions and related ones ∗
We prove that many of beta, beta prime, gamma, inverse gamma, Student tand 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, many of ultraspherical and Student t-distributions have free divisibility indicator 1.
متن کاملProgramming infinite machines
For infinite machines which are free from the classical Thompson’s lamp paradox we show that they are not free from its inverted version. We provide a program for infinite machines and an infinite mechanism which simulate this paradox. While their finite analogs work predictably, the program and the infinite mechanism demonstrate an undefined behavior. As in the case of infinite Davies’s machin...
متن کاملInfinitely Divisible Distributions for Rectangular Free Convolution: Classification and Matricial Interpretation
In a previous paper ([B-G1]), we defined the rectangular free convolution ⊞ λ . Here, we investigate the related notion of infinite divisibility, which happens to be closely related the classical infinite divisibility: there exists a bijection between the set of classical symmetric infinitely divisible distributions and the set of ⊞ λ -infinitely divisible distributions, which preserves limit t...
متن کاملOn a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions
In this paper, we prove a result linking the square and the rectangular R-transforms, which consequence is a surprising relation between the square and rectangular free convolutions, involving the Marchenko-Pastur law. Consequences on infinite divisibility and on the arithmetics of Voiculescu’s free additive and multiplicative convolutions are given.
متن کامل