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- W2962980368 endingPage "810" @default.
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- W2962980368 abstract "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." @default.
- W2962980368 created "2019-07-30" @default.
- W2962980368 creator A5060156386 @default.
- W2962980368 date "2019-05-03" @default.
- W2962980368 modified "2023-10-18" @default.
- W2962980368 title "Percolation on Hyperbolic Graphs" @default.
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- W2962980368 doi "https://doi.org/10.1007/s00039-019-00498-0" @default.
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