3 problems

Let $\mathcal{L}_{\alpha}^{\infty}$ be the infinite stable looptree, with root $\rho$, metric ball $B(\rho,r)$, and effective resistance metric $R_{\mathrm{eff}}$. The source estab…

Let $\mathcal{L}_{\alpha}$ be a compact stable looptree with intrinsic measure $\nu$, normalized by $\nu(\mathcal{L}_{\alpha})=1$, and let $B(\rho,r)$ and $\bar{B}(\rho,r)$ denote…

The Uniform Infinite Half-Planar Triangulation has an incipient infinite cluster whose boundary converges, after rescaling, to the infinite stable looptree…