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arXiv · 2311.13178

Combinatorics of cyclic-conditional freeness

Octavio Arizmendi·Guillaume Cébron·Nicolas Gilliers
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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.

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Octavio Arizmendi, Guillaume Cébron, Nicolas Gilliers. 2023-11-22. Combinatorics of cyclic-conditional freeness. https://arxiv.org/abs/2311.13178

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