An alternating moment condition for bi-freeness
Operator Algebras
2019-02-18 v3
Abstract
In this note we demonstrate an equivalent condition for bi-freeness, inspired by the well-known "vanishing of alternating centred moments" condition from free probability. We show that all products satisfying a centred condition on maximal monochromatic \chi-intervals have vanishing moments if and only if the family of pairs of faces they come from is bi-free, and show that similar characterisations hold for the amalgamated and conditional settings. In addition, we construct a bi-free unitary Brownian motion and show that conjugation by this process asymptotically creates bi-freeness; these considerations lead to another characterisation of bi-free independence.
Keywords
Cite
@article{arxiv.1611.01262,
title = {An alternating moment condition for bi-freeness},
author = {Ian Charlesworth},
journal= {arXiv preprint arXiv:1611.01262},
year = {2019}
}
Comments
Updated to accepted manuscript. 15 pages, 4 figures. Comments welcome