Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetry in supercritical bond percolation in dimensions three and
  higher   We study the isoperimetric subgraphs of the infinite cluster
$\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with
$d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap
[-n,n]^d$ which have minimal open edge boundary to volume ratio. We prove a
shape theorem for these subgraphs, obtaining that when suitably rescaled, these
subgraphs converge almost surely to a translate of a deterministic shape. This
deterministic shape is itself an isoperimetric set for a norm we construct. As
a corollary, we obtain sharp asymptotics on a natural modification of the
Cheeger constant for $\textbf{C}_\infty \cap [-n,n]^d$. This settles a
conjecture of Benjamini for the version of the Cheeger constant defined here.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ