Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On chemical distances and shape theorems in percolation models with
  long-range correlations   In this paper we provide general conditions on a one parameter family of
random infinite subsets of Z^d to contain a unique infinite connected component
for which the chemical distances are comparable to the Euclidean distances,
focusing primarily on models with long-range correlations. Our results are in
the spirit of those by Antal and Pisztora proved for Bernoulli percolation. We
also prove a shape theorem for balls in the chemical distance under such
conditions. Our general statements give novel results about the structure of
the infinite connected component of the vacant set of random interlacements and
the level sets of the Gaussian free field. We also obtain alternative proofs to
the main results in arXiv:1111.3979. Finally, as a corollary, we obtain new
results about the (chemical) diameter of the largest connected component in the
complement of the trace of the random walk on the torus.

14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an