Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrence for vertex-reinforced random walks on Z with weak
  reinforcements   We prove that any vertex-reinforced random walk on the integer lattice with
non-decreasing reinforcement sequence $w$ satisfying $w(k) = o(k^{\alpha})$ for
some $\alpha < 1/2$ is recurrent. This improves on previous results of Volkov
(2006) and Schapira (2012).

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ