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math.OA2023
Infinitesimal Operators and the Distribution of Anticommutators and Commutators
James A. Mingo, Pei-Lun Tseng
In an infinitesimal probability space we consider operators which are infinitesimally free and one of which is infinitesimal, in that all its moments vanish. Many previously analys…
math.OA2020
On operator-valued infinitesimal Boolean and monotone independence
Daniel Perales, Pei-Lun Tseng
We introduce the notion of operator-valued infinitesimal (OVI) independence for the Boolean and monotone cases. Then show that OVI Boolean (resp. monotone) independence is equivale…