Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on recurrence of the Vertex reinforced jump process and
  fractional moments localization   We give a simple proof for recurrence of vertex reinforced jump process on
\(\mathbb{Z}^d\), under strong reinforcement. Moreover, we show how the
previous result implies that linearly edge-reinforced random walk on \
\(\mathbb{Z}^d\) is {recurrent} for strong reinforcement. Finally, we prove
that the \(H^{(2|2)}\) model on \(\mathbb{Z}^d\) localizes at strong disorder.
Even though these results are well-known, we propose a unified approach, {which
also has the advantage to provide shorter proofs}, and relies on estimating
fractional moments, introduced by Aizenman and Molchanov.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci