Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge-reinforced random walk, Vertex-Reinforced Jump Process and the
  supersymmetric hyperbolic sigma model   Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in
1986, is a random process, which takes values in the vertex set of a graph $G$,
and is more likely to cross edges it has visited before. We show that it can be
represented in terms of a Vertex-reinforced jump process (VRJP) with
independent gamma conductances: the VRJP was conceived by Werner and first
studied by Davis and Volkov (2002,2004), and is a continuous-time process
favouring sites with more local time. We calculate, for any finite graph $G$,
the limiting measure of the centred occupation time measure of VRJP, and
interpret it as a supersymmetric hyperbolic sigma model in quantum field
theory, introduced by Zirnbauer (1991). This enables us to deduce that VRJP and
ERRW are positive recurrent in any dimension for large reinforcement, and that
VRJP is transient in dimension greater than or equal to 3 for small
reinforcement, using results of Disertori and Spencer (2010), Disertori,
Spencer and Zirnbauer (2010).

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
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys