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math.PR2018★ 29 cited
Existence of phase transition for percolation using the Gaussian Free Field
Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi +2
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension undergoes a non-trivial phase transition (in the sense that ).…
math.PR2018
Strict monotonicity of percolation thresholds under covering maps
Sébastien Martineau, Franco Severo
We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph strictly increases the value of its percolation critical parameter $p…