2 problems

Let $(\mathcal{G}^n)_{n\geq 0}$ be a family of $d$-regular graphs with $|\mathcal{G}^n|\to\infty$. For each $n$, form the cylinder graph $\mathcal{G}^n\times\mathbb{N}$, let…

Let $cmathcal{E}_n$ be the external DLA cluster on $cmathbb{Z}^d$ started from $cmathcal{E}_0=\{0\}$, and let $r(cmathcal{E}_n)$ denote its radius. External DLA radius-growth conje…