New characterization of two-state normal distribution
Functional Analysis
2016-09-06 v1
Abstract
In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional expectation in free probability, but has no classical analogue. We also show a generalization of Bozejko, Leinert and Speicher's formula (relating moments and noncommutative cumulants).
Keywords
Cite
@article{arxiv.1401.0307,
title = {New characterization of two-state normal distribution},
author = {Wiktor Ejsmont},
journal= {arXiv preprint arXiv:1401.0307},
year = {2016}
}
Comments
19 pages, 2 figures, accepted for publication by Infinite Dimensional Analysis, Quantum Probability and Related Topics