2010/09/13 by Fevrier, Maxime · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)
paper · doi:10.48550/arxiv.1009.2389
We define higher order infinitesimal noncommutative probability space and infinitesimal non-crossing cumulant functionals. In this framework, we generalize to higher order the notion of infinitesimal freeness, via a vanishing of mixed cumulants condition. We also introduce and study some non-crossing partitions related to this notion. Finally, as an application, we show how to compute the successive derivatives of the free convolution of two time-indexed families of distributions from their individual derivatives.