Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Return probability and recurrence for the random walk driven by
  two-dimensional Gaussian free field   Given any $\gamma>0$ and for $\eta=\{\eta_v\}_{v\in \mathbb Z^2}$ denoting a
sample of the two-dimensional discrete Gaussian free field on $\mathbb Z^2$
pinned at the origin, we consider the random walk on~$\mathbb Z^2$ among random
conductances where the conductance of edge $(u, v)$ is given by
$\mathrm{e}^{\gamma(\eta_u + \eta_v)}$. We show that, for almost every~$\eta$,
this random walk is recurrent and that, with probability tending to~1 as $T\to
\infty$, the return probability at time~$2T$ decays as $T^{-1+o(1)}$. In
addition, we prove a version of subdiffusive behavior by showing that the
expected exit time from a ball of radius~$N$ scales as $N^{\psi(\gamma)+o(1)}$
with $\psi(\gamma)>2$ for all~$\gamma>0$. Our results rely on delicate control
of the effective resistance for this random network. In particular, we show
that the effective resistance between two vertices at Euclidean distance~$N$
behaves as~$N^{o(1)}$.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th