Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-directed polymers in heavy-tail random environment in dimension
  $d\geq 2$   In this article we study a \emph{non-directed} polymer model in dimension
$d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which
interacts with a random environment, represented by i.i.d. random variables
$(\omega_x)_{x\in \mathbb{Z}^d}$. The model consists in modifying the law of
the random walk up to time (or length) $N$ by the exponential of $\sum_{x\in
\mathcal{R}_N}\beta (\omega_x-h)$ where $\mathcal{R}_N$ is the range of the
walk, \textit{i.e.} the set of visited sites up to time $N$, and $\beta\geq
0,\, h\in \mathbb{R}$ are two parameters. We study the behavior of the model in
a weak-coupling regime, that is taking $\beta:=\beta_N$ vanishing as the length
$N$ goes to infinity, and in the case where the random variables $\omega$ have
a heavy tail with exponent $\alpha\in (0,d)$. We are able to obtain precisely
the behavior of polymer trajectories under all possible weak-coupling regimes
$\beta_N = \hat \beta N^{-\gamma}$ with $\gamma \geq 0$: we find the correct
transversal fluctuation exponent $\xi$ for the polymer (it depends on $\alpha$
and $\gamma$) and we give the limiting distribution of the rescaled
log-partition function. This extends existing works to the non-directed case
and to higher dimensions.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs