Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delocalising the parabolic Anderson model through partial duplication of
  the potential   The parabolic Anderson model on $\mathbb{Z}^d$ with i.i.d. potential is known
to completely localise if the distribution of the potential is sufficiently
heavy-tailed at infinity. In this paper we investigate a modification of the
model in which the potential is partially duplicated in a symmetric way across
a plane through the origin. In the case of potential distribution with
polynomial tail decay, we exhibit a surprising phase transition in the model as
the decay exponent varies. For large values of the exponent the model
completely localises as in the i.i.d. case. By contrast, for small values of
the exponent we show that the model may delocalise. More precisely, we show
that there is an event of non-negligible probability on which the solution has
non-negligible mass on two sites.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas