Higher order infinitesimal freeness
Operator Algebras
2010-09-14 v1 Combinatorics
Probability
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.
Keywords
Cite
@article{arxiv.1009.2389,
title = {Higher order infinitesimal freeness},
author = {Maxime Fevrier},
journal= {arXiv preprint arXiv:1009.2389},
year = {2010}
}
Comments
38 pages