Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The boundary action of a sofic random subgroup of the free group   We prove that the boundary action of a sofic random subgroup of a finitely
generated free group is conservative. This addresses a question asked by
Grigorchuk, Kaimanovich, and Nagnibeda, who studied the boundary actions of
individual subgroups of the free group. Following their work, we also
investigate the cogrowth and various limit sets associated to sofic random
subgroups. We make heavy use of the correspondence between subgroups and their
Schreier graphs, and central to our approach is an investigation of the
asymptotic density of a given set inside of large neighborhoods of the root of
a sofic random Schreier graph.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess