Characterization of non-commutative free Gaussian variables

Article Type

Research Article

Publication Title

Alea

Abstract

We provide a necessary and sufficient condition, based on zero correlation, for self-adjoint, freely independent, identically distributed random variables on a *-probability space to be free Gaussian. Along the way, we establish a free analogue of a well known application of Basu's theorem from statistics. We also show that all linear combinations of free Gaussian being free Gaussian does not necessarily imply joint free Gaussianity, and we identify additional conditions under which this implication is true.

First Page

1241

Last Page

1255

DOI

10.30757/ALEA.V15-46

Publication Date

1-1-2018

Comments

All Open Access, Bronze

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