Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing of the anchored isoperimetric profile in bond percolation at p
  c   We consider the anchored isoperimetric profile of the infinite open cluster,
defined for $p > p\_c$, whose existence has been recently proved in [3]. We
extend adequately the definition for $p = p\_c$, in finite boxes. We prove a
partial result which implies that, if the limit defining the anchored
isoperimetric profile at $p\_c$ exists, it has to vanish.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga