Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A branching process approach to level-$k$ phylogenetic networks   The mathematical analysis of random phylogenetic networks via analytic and
algorithmic methods has received increasing attention in the past years. In the
present work we introduce branching process methods to their study. This
approach appears to be new in this context. Our main results focus on random
level-$k$ networks with $n$ labelled leaves. Although the number of
reticulation vertices in such networks is typically linear in $n$, we prove
that their asymptotic global and local shape is tree-like in a well-defined
sense. We show that the depth process of vertices in a large network converges
towards a Brownian excursion after rescaling by $n^{-1/2}$. We also establish
Benjamini--Schramm convergence of large random level-$k$ networks towards a
novel random infinite network.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex