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On the effect of adding epsilon-Bernoulli percolation to everywhere percolating subgraphs of Z^d

Itai Benjamini·Olle Häggström·Oded Schramm
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Abstract

We show that adding epsilon-Bernoulli percolation to an everywhere percolating subgraph of Z^2 results in a graph which has large scale geometry similar to that of supercritical Bernoulli percolation, in various specific senses. We conjecture similar behavior in higher dimensions.

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Itai Benjamini, Olle Häggström, Oded Schramm. 1999-06-01. On the effect of adding epsilon-Bernoulli percolation to everywhere percolating subgraphs of Z^d. https://doi.org/10.1063/1.533187

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