Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants

Celestino, Adrian; Ebrahimi‐Fard, Kurusch; Nica, Alexandru; Perales, Daniel; Witzman, Leon

doi:10.1016/j.aam.2022.102481

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Relation With T-cumulants1

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“…A natural question follows by considering the relation between the distribution B t (Φ) and t-Boolean cumulants. In this situation, we can prove a claim remarked in [8,Rmk. 11.9] which states that t-Boolean cumulants of B t (Φ) are given precisely by the Boolean cumulants of Φ.…”

Section: Relation With T-cumulantssupporting

confidence: 59%

Relations between infinitesimal non-commutative cumulants

2021

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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.

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Section: Relation With T-cumulantssupporting

confidence: 59%