Geodesic
Relations between infinitesimal non-commutative cumulants
Documenta mathematica, Tome 26 (2021), pp. 1145-1185

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Boolean, free and monotone cumulants as well as relations among them, have proven to be important in the study of non-commutative probability theory. Quite notably, Boolean cumulants were successfully used to study free infinite divisibility via the Boolean Bercovici-Pata bijection. On the other hand, in recent years the concept of infinitesimal non-commutative probability has been developed, together with the notion of infinitesimal cumulants which can be useful in the context of combinatorial questions.
DOI : 10.4171/dm/838
Classification : 16T05, 16T30, 46L53, 46L54
Mots-clés : Hopf algebra, infinitesimal non-commutative probability theory, infinitesimal cumulants, cumulant-cumulant relations 
Adrián Celestino; Daniel Perales; Kurusch Ebrahimi-Fard. Relations between infinitesimal non-commutative cumulants. Documenta mathematica, Tome 26 (2021), pp. 1145-1185. doi: 10.4171/dm/838
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     author = {Adri\'an Celestino and Daniel Perales and Kurusch Ebrahimi-Fard},
     title = {Relations between infinitesimal non-commutative cumulants},
     journal = {Documenta mathematica},
     pages = {1145--1185},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/838},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/838/}
}
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