Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unicellular maps vs hyperbolic surfaces in large genus: simple closed
  curves   We study uniformly random maps with a single face, genus $g$, and size $n$,
as $n,g\rightarrow \infty$ with $g = o(n)$, in continuation of several previous
works on the geometric properties of "high genus maps". We calculate the number
of short simple cycles, and we show convergence of their lengths (after a
well-chosen rescaling of the graph distance) to a Poisson process, which
happens to be exactly the same as the limit law obtained by Mirzakhani and
Petri (2019) when they studied simple closed geodesics on random hyperbolic
surfaces under the Weil-Petersson measure as $g\rightarrow \infty$. This leads
us to conjecture that these two models are somehow "the same" in the limit,
which would allow to translate problems on hyperbolic surfaces in terms of
random trees, thanks to a powerful bijection of Chapuy, F\'eray and Fusy
(2013).

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys