Combinatorics of cyclic-conditional freeness

Fuente: arXiv
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Main Authors: Arizmendi, Octavio, Cébron, Guillaume, Gilliers, Nicolas
Format: Preprint
Published: 2023
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author Arizmendi, Octavio
Cébron, Guillaume
Gilliers, Nicolas
author_facet Arizmendi, Octavio
Cébron, Guillaume
Gilliers, Nicolas
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_13178
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Combinatorics of cyclic-conditional freeness
Arizmendi, Octavio
Cébron, Guillaume
Gilliers, Nicolas
Operator Algebras
Probability
46L53, 46L54
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.
title Combinatorics of cyclic-conditional freeness
topic Operator Algebras
Probability
46L53, 46L54
url https://arxiv.org/abs/2311.13178