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- W2580323439 abstract "The theory of cumulants is revisited in the Rota way, that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular combinatorial Hopf algebra. The latter is neither commutative nor cocommutative, and has an underlying unshuffle bialgebra structure which gives rise to a shuffle product on its graded dual. The moment-cumulant relations are encoded in terms of shuffle and half-shuffle exponentials. It is then shown how to express concisely monotone, free, and boolean cumulants in terms of each other using the pre-Lie Magnus expansion together with shuffle and half-shuffle logarithms." @default.
- W2580323439 created "2017-02-03" @default.
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- W2580323439 date "2018-04-01" @default.
- W2580323439 modified "2023-10-09" @default.
- W2580323439 title "Monotone, free, and boolean cumulants: A shuffle algebra approach" @default.
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- W2580323439 doi "https://doi.org/10.1016/j.aim.2018.01.003" @default.
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