IUMJ

Title: Higher order infinitesimal freeness

Authors: Maxime Fevrier

Issue: Volume 61 (2012), Issue 1, 249-295

Abstract:

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.