3 problems

Let $(A_n)_{n\geq 0}$ be the DLA cluster process in the wedge $W_{\theta_1,\theta_2}$, and define its growth rate by … where $\operatorname{diam}$ denotes Euclidean diameter, and l…

Let $A_\infty$ be the limiting diffusion-limited aggregation cluster in a wedge, and interpret its arms as the ends of the graph $A_\infty$. One-arm conjecture. There exists…

Let $\Omega$ be a simply connected open domain in the plane, and let $A,B,C,D$ be four boundary points of $\Omega$ in clockwise order. For critical percolation on the $1/n$-scaled…