Greedy lattice paths with general weights

Yinshan Chang, Anqi Zheng

Let $\{X_v:v\in {\mathbb{Z}}^d\}$ be i.i.d. random variables. Let $S(\pi )={\sum }_{v\in \pi }{X}_v$ be the weight of a self-avoiding lattice path $\pi$. Let \[M_n=\max\{S(π):π\text{ has length }…