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arXiv · 2312.04614

Conditionally monotone cumulants via shuffle algebra

Adrian Celestino·Kurusch Ebrahimi-Fard
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Abstract

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.

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BibTeXRIS

Adrian Celestino, Kurusch Ebrahimi-Fard. 2023-12-07. Conditionally monotone cumulants via shuffle algebra. https://doi.org/10.1142/s0219025724500176

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