2 problems

Let $k \in \mathbb{Z}_{\geq 1}$. Let $\mu$ be a translation-invariant, ergodic, finite-energy, $k$-dependent edge percolation measure on $\mathbb{Z}^2$. Full-plane trichotomy conje…

Let $\Phi=(\Phi_x)_{x\in\mathbb{Z}^d}$ be the massless Gaussian free field on $\mathbb{Z}^d$, with $d\geqslant 3$. For $h\in\mathbb{R}$, let…