# Characterizations of Some Free Random Variables by Properties of Conditional Moments of Third Degree Polynomials

Journal of Theoretical Probability, Jul 2013

We investigate Laha–Lukacs properties of noncommutative random variables (processes). We prove that some families of free Meixner distributions can be characterized by the conditional moments of polynomial functions of degree 3. We also show that this fact has consequences in describing some free Lévy processes. The proof relies on a combinatorial identity. At the end of this paper we show that this result can be extended to a $q$-Gausian variable.

This is a preview of a remote PDF: http://link.springer.com/content/pdf/10.1007%2Fs10959-012-0467-7.pdf

Wiktor Ejsmont. Characterizations of Some Free Random Variables by Properties of Conditional Moments of Third Degree Polynomials, Journal of Theoretical Probability, 2014, 915-931, DOI: 10.1007/s10959-012-0467-7