Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A construction which relates c-freeness to infinitesimal freeness   We consider two extensions of free probability that have been studied in the
research literature, and are based on the notions of c-freeness and
respectively of infinitesimal freeness for noncommutative random variables. In
a 2012 paper, Belinschi and Shlyakhtenko pointed out a connection between these
two frameworks, at the level of their operations of 1-dimensional free additive
convolution. Motivated by that, we propose a construction which produces a
multi-variate version of the Belinschi-Shlyakhtenko result, together with a
result concerning free products of multi-variate noncommutative distributions.
Our arguments are based on the combinatorics of the specific types of cumulants
used in c-free and in infinitesimal free probability. They work in a rather
general setting, where the initial data consists of a vector space $V$ given
together with a linear map $\Delta : V \to V \otimes V$. In this setting, all
the needed brands of cumulants live in the guise of families of multilinear
functionals on $V$, and our main result concerns a certain transformation
$\Delta^{*}$ on such families of multilinear functionals.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga