Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Products of free random variables and k-divisible partitions   We derive a formula for the moments and the free cumulants of the
multiplication of $k$ free random variables in terms of $k$-equal and
$k$-divisible non-crossing partitions. This leads to a new simple proof for the
bounds of the right-edge of the support of the free multiplicative convolution
$\mu^{\boxtimes k}$, given by Kargin which show that the support grows at most
linearly with $k$. Moreover, this combinatorial approach generalize the results
of Kargin since we do not require the convolved measures to be identical. We
also give further applications, such as a new proof of the limit theorem of
Sakuma and Yoshida.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph