English

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

R2 v1 2026-06-22T02:37:56.655Z