Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic isoperimetry of the giant component of supercritical bond
  percolation in dimension two   We study the isoperimetric subgraphs of the giant component $\textbf{C}_n$ of
supercritical bond percolation on the square lattice. These are subgraphs of
$\textbf{C}_n$ having minimal edge boundary to volume ratio. In contrast to the
work of Biskup, Louidor, Procaccia and Rosenthal, the edge boundary is taken
only within $\textbf{C}_n$ instead of the full infinite cluster. The
isoperimetric subgraphs are shown to converge almost surely, after rescaling,
to the collection of optimizers of a continuum isoperimetric problem emerging
naturally from the model. We also show that the Cheeger constant of
$\textbf{C}_n$ scales to a deterministic constant, which is itself an
isoperimetric ratio, settling a conjecture of Benjamini in dimension two.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
7
The categories of this paper are: hep-th