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• W2285840135 abstract "In this paper we study percolation on a roughly transitive graph G with polynomial growth and isoperimetric dimension larger than one. For these graphs we are able to prove that p_c < 1, or in other words, that there exists a percolation phase. The main results of the article work for both dependent and independent percolation processes, since they are based on a quite robust renormalization technique. When G is transitive, the fact that p_c < 1 was already known before. But even in that case our proof yields some new results and it is entirely probabilistic, not involving the use of Gromov's theorem on groups of polynomial growth. We finish the paper giving some examples of dependent percolation for which our results apply." @default.
• W2285840135 created "2016-06-24" @default.
• W2285840135 creator A5044402376 @default.
• W2285840135 creator A5059860426 @default.
• W2285840135 date "2015-07-28" @default.
• W2285840135 modified "2023-09-27" @default.
• W2285840135 title "Percolation and isoperimetry on roughly transitive graphs" @default.
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• W2285840135 hasPublicationYear "2015" @default.
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