Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walks and quasi-convexity in acylindrically hyperbolic groups   It is known that every infinite index quasi-convex subgroup $H$ of a
non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex
subgroup of $G$. We give a probabilistic generalization of this result. That
is, we show that when $R$ is a subgroup generated by independent random walks
in $G$, then $\langle H, R\rangle\cong H\ast R$ with probability going to one
as the lengths of the random walks go to infinity and this subgroup is
quasi-convex in $G$. Moreover, our results hold for a large class of groups
acting on hyperbolic metric spaces and subgroups with quasi-convex orbits. In
particular, when $G$ is the mapping class group of a surface and $H$ is a
convex cocompact subgroup we show that $\langle H, R\rangle$ is convex
cocompact and isomorphic to $ H\ast R$.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an