Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Percolation on hyperbolic graphs   We prove that Bernoulli bond percolation on any nonamenable, Gromov
hyperbolic, quasi-transitive graph has a phase in which there are infinitely
many infinite clusters, verifying a well-known conjecture of Benjamini and
Schramm (1996) under the additional assumption of hyperbolicity. In other
words, we show that $p_c<p_u$ for any such graph. Our proof also yields that
the triangle condition $\nabla_{p_c}<\infty$ holds at criticality on any such
graph, which is known to imply that several critical exponents exist and take
their mean-field values. This gives the first family of examples of one-ended
groups all of whose Cayley graphs are proven to have mean-field critical
exponents for percolation.

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The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat