3 problems

Excursion-decomposition scaling-limit conjecture. The discrete decompositions converge to a decomposition $(E_k,\theta_k,\mu_k)_{k\geq 1}$ such that the union of outermost positive…

Let $f$ satisfy Assumptions and, and suppose there exist $\alpha\in(0,2)$ and $r_0>0$ such that … for all $|x|<r_0$. Let $D\subset\mathbb{R}^2$ be an open rectangle centred at the…

Let $f$ satisfy Assumptions,, and, and let $D\subset\mathbb{R}^2$ be an open rectangle centred at the origin. Write $D_R$ for its dilation by $R$, and let $N_\mathrm{ES}(D_R,\ell)$…