Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415120 | Journal of Functional Analysis | 2014 | 19 Pages |
Abstract
Dual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-binomial non-commutative variables which are free. Second, we give a characterization of non-commutative free-Poisson and free-binomial variables by properties of first two conditional moments, which mimic Lukacs type assumptions known from classical probability. More precisely, our result is a non-commutative version of the following result known in classical probability: if U, V are independent real random variables, such that E(V(1âU)|UV) and E(V2(1âU)2|UV) are non-random then V has a gamma distribution and U has a beta distribution.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kamil Szpojankowski, Jacek WesoÅowski,