Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernoulli and self-destructive percolation on non-amenable graphs   In this note we study some properties of infinite percolation clusters on
non-amenable graphs. In particular, we study the percolative properties of the
complement of infinite percolation clusters. An approach based on
mass-transport is adapted to show that for a large class of non-amenable
graphs, the graph obtained by removing each site contained in an infinite
percolation cluster has critical percolation threshold which can be arbitrarily
close to the critical threshold for the original graph, almost surely, as p
approaches p_c. Closely related is the self-destructive percolation process,
introduced by J. van den Berg and R. Brouwer, for which we prove that an
infinite cluster emerges for any small reinforcement.

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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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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: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio