Combinatorics of cyclic-conditional freeness
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917283143614464 |
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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 |