Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integer moments of complex Wishart matrices and Hurwitz numbers   We give formulae for the cumulants of complex Wishart (LUE) and inverse
Wishart matrices (inverse LUE). Their large-$N$ expansions are generating
functions of double (strictly and weakly) monotone Hurwitz numbers which count
constrained factorisations in the symmetric group. The two expansions can be
compared and combined with a duality relation proved in [F. D. Cunden, F.
Mezzadri, N. O'Connell and N. J. Simm, arXiv:1805.08760] to obtain: i) a
combinatorial proof of the reflection formula between moments of LUE and
inverse LUE at genus zero and, ii) a new functional relation between the
generating functions of monotone and strictly monotone Hurwitz numbers. The
main result resolves the integrality conjecture formulated in [F. D. Cunden, F.
Mezzadri, N. J. Simm and P. Vivo, J. Phys. A 49 (2016)] on the time-delay
cumulants in quantum chaotic transport. The precise combinatorial description
of the cumulants given here may cast new light on the concordance between
random matrix and semiclassical theories.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph