2 problems

Let $\gamma_{0}^\star=(0,v_1^\star,v_2^\star,\dots):=\arg\min\{\lvert\gamma_L\rvert\}$ be the shortest exploding path starting at $0$, where $\lvert\gamma_L\rvert$ denotes its $L$-…

Let $d_L(x,y)$ denote the $L$-distance between vertices $x,y\in\mathbb{Z}^d$, and let $V_x$ be the explosion time from $x$. Under the condition of the distance theorem, these quant…