Phase transition for level-set percolation of the membrane model in dimensions $d\ge 5$

Alberto Chiarini, Maximilian Nitzschner

We consider level-set percolation for the Gaussian membrane model on ${\mathbb{Z}}^d$, with $d\ge 5$, and establish that as $h\in \mathbb{R}$ varies, a non-trivial percolation pha…