Conditionally monotone cumulants via shuffle algebra
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912293875351552 |
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| author | Celestino, Adrian Ebrahimi-Fard, Kurusch |
| author_facet | Celestino, Adrian Ebrahimi-Fard, Kurusch |
| contents | In this work we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as an infinitesimal character and identify the c-monotone additive convolution as an associative operation in the set of pairs of characters in the dual of a double tensor Hopf algebra. In this algebraic framework, we understand previous results on c-monotone cumulants and prove a combinatorial formula that relates c-free and c-monotone cumulants. We also identify the notion of $t$-Boolean cumulants in the shuffle-algebraic approach and introduce the corresponding notion of $t$-monotone cumulants as a particular case of c-monotone cumulants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_04614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditionally monotone cumulants via shuffle algebra Celestino, Adrian Ebrahimi-Fard, Kurusch Operator Algebras Combinatorics Probability Rings and Algebras 05E99, 16T30, 17A30, 46L53 In this work we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as an infinitesimal character and identify the c-monotone additive convolution as an associative operation in the set of pairs of characters in the dual of a double tensor Hopf algebra. In this algebraic framework, we understand previous results on c-monotone cumulants and prove a combinatorial formula that relates c-free and c-monotone cumulants. We also identify the notion of $t$-Boolean cumulants in the shuffle-algebraic approach and introduce the corresponding notion of $t$-monotone cumulants as a particular case of c-monotone cumulants. |
| title | Conditionally monotone cumulants via shuffle algebra |
| topic | Operator Algebras Combinatorics Probability Rings and Algebras 05E99, 16T30, 17A30, 46L53 |
| url | https://arxiv.org/abs/2312.04614 |