Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Summing free unitary random matrices   I use quaternion free probability calculus - an extension of free probability
to non-Hermitian matrices (which is introduced in a succinct but self-contained
way) - to derive in the large-size limit the mean densities of the eigenvalues
and singular values of sums of independent unitary random matrices, weighted by
complex numbers. In the case of CUE summands, I write them in terms of two
"master equations," which I then solve and numerically test in four specific
cases. I conjecture a finite-size extension of these results, exploiting the
complementary error function. I prove a central limit theorem, and its first
sub-leading correction, for independent identically-distributed zero-drift
unitary random matrices.

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg