The sign clusters of the massless Gaussian free field percolate on ${\mathbb{Z}}^d$, $d⩾3$ (and more)

Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez

We investigate the percolation phase transition for level sets of the Gaussian free field on ${\mathbb{Z}}^d$, with $d⩾3$, and prove that the corresponding critical paramete…