Combinatorics of cyclic-conditional freeness
Operator Algebras
2026-02-23 v3 Probability
Abstract
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolution. In the process, we establish the notion of "cyclic freeness", demonstrating its equivalence to infinitesimal freeness in the presence of tracial states. Furthermore, we show that cyclic conditional freeness can be reduced to cyclic freeness through a multivariate extension of the inverse Markov-Krein transform.
Cite
@article{arxiv.2311.13178,
title = {Combinatorics of cyclic-conditional freeness},
author = {Octavio Arizmendi and Guillaume Cébron and Nicolas Gilliers},
journal= {arXiv preprint arXiv:2311.13178},
year = {2026}
}