4 problems

Let $D$ be a simply connected domain, let $a,b\in\partial D$ be distinct boundary points, and consider the chordal $\textrm{SLE}_\kappa$ trace from $a$ to $b$, modulo reparameteriz…

Let $G_n$ be the partially wired square grid described in the source, let $\omega$ have the critical random-cluster measure with $q\in(0,4)$, let $\omega^\dagger$ be its dual confi…

Let $\mathbb{U}$ be the unit disk and consider a square grid of mesh $\epsilon$. Let the uniform measure be taken on simple grid paths from $0$ to $\partial\mathbb{U}$, and separat…

Let $\gamma$ be the trace of chordal $\textrm{SLE}_\kappa$ in the upper half-plane. SLE8 trace continuity conjecture. For $\kappa=8$, the trace $\gamma$ is almost surely a continuo…