• Corpus ID: 240354129

Gap at 1 for the percolation threshold of Cayley graphs

  title={Gap at 1 for the percolation threshold of Cayley graphs},
  author={Christoforos Panagiotis and Franco Severo},
We prove that the set of possible values for the percolation threshold p c of Cayley graphs has a gap at 1 in the sense that there exists ε 0 > 0 such that for every Cayley graph G one either has p c ( G ) = 1 or p c ( G ) ≤ 1 − ε 0 . The proof builds on the new approach of Duminil-Copin, Goswami, Raoufi, Severo & Yadin ( Duke Math. J., 2020 ) to the existence of phase transition using the Gaussian free field, combined with the finitary version of Gromov’s theorem on the structure of groups of… 
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