Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the set of critical exponents of discrete groups acting on regular
  trees   We study the set of critical exponents of discrete groups acting on regular
trees. We prove that for every real number $\delta$ between $0$ and
$\frac{1}{2}\log q$, there is a discrete subgroup $\Gamma$ acting without
inversion on a $(q+1)$-regular tree whose critical exponent is equal to
$\delta$. Explicit construction of edge-indexed graphs corresponding to a
quotient graph of groups are given.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con