Franco Severo

collaborators

4 papers

math.PR2021

Gap at 1 for the percolation threshold of Cayley graphs

Christoforos Panagiotis, 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 Ca…

math.PR2021

Sharp phase transition for Gaussian percolation in all dimensions

Franco Severo

We consider the level-sets of continuous Gaussian fields on $R^{d}$ above a certain level $- ℓ \in R$ , which defines a percolation model as $ℓ$ varies. We assum…

math.PR2018

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 $d > 4$ undergoes a non-trivial phase transition (in the sense that $p_{c} < 1$ ).…

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…