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arXiv · 1401.0307

New characterization of two-state normal distribution

Wiktor Ejsmont
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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).

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Wiktor Ejsmont. 2014-01-01. New characterization of two-state normal distribution. https://doi.org/10.1142/s0219025714500192

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