Bond percolation does not simulate site percolation
We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of a vertex of degree $3$ cannot be simulated even approximately by bond percolation, and develop a decision tree techniqu...
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Zusammenfassung: | We show that a site percolation is a stronger model than a bond percolation.
We use the van den Berg -- Kesten (vdBK) inequality to prove that site
percolation on a neighborhood of a vertex of degree $3$ cannot be simulated
even approximately by bond percolation, and develop a decision tree technique
to prove the same for a neighborhood of a vertex of degree $2$. This technique
can be used to obtain inequalities for connectedness probabilities, including a
conjectured inequality of Erik Aas. |
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DOI: | 10.48550/arxiv.2404.08873 |