2 problems

Bogomolny–Schmit conjecture. Their nodal lines at large scales should converge to curves described by Schramm–Loewner evolution with parameter $6$, namely $\operatorname{SLE}_6$.

Let ${\bf R}_{\pi\epsilon,\pi}$ be the rectangle with side lengths $\pi\epsilon$ and $\pi$, and let $\mathfrak L_3(\epsilon)$ denote its minimal 3-partition energy. For…