Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharpness versus robustness of the percolation transition in 2D contact
  processes   We study versions of the contact process with three states, and with
infections occurring at a rate depending on the overall infection density.
Motivated by a model described in [17] for vegetation patterns in arid
landscapes, we focus on percolation under invariant measures of such processes.
We prove that the percolation transition is sharp (for one of our models this
requires a reasonable assumption). This is shown to contradict a form of
'robust critical behaviour' with power law cluster size distribution for a
range of parameter values, as suggested in [17].

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int