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Critical level set percolation for the GFF in $d>6$: comparison principles and some consequences

Critical level set percolation for the GFF in $d>6$: comparison principles and some consequences

In this paper we study the intrinsic geometry of the critical percolation cluster induced by the level set of the metric Gaussian free field on $\mathbb{Z}^d$ above the critical dimension of six. (Lupu, 2016) established that the critical percolation cluster has the same law as that in a Poisson loop …