Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On star-Moments of the compression of the free unitary Brownian motion
  by a free projection   In this paper, we derive explicit expressions for the moments and for the
mixed moments of the compression of a free unitary Brownian motion by a free
projection. While the moments of this non-normal operator are readily derived
using analytical or combinatorial methods, we only succeeded to derive its
mixed ones after solving a non-linear partial differential equation for their
two-variables generating function. Nonetheless, the combinatorics of non
crossing partitions lead to another expression of the lowest-order mixed
moment. We shall also give some interest in odd alternating moments. In
particular, we derive a linear partial differential equation for their
generating function and discuss the combinatorial approach to these moments
when the rank of the projection equals $1/2$.

10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th