Limiting geodesics for first-passage percolation on subsets of $\mathbb{Z}^{2}$
Limiting geodesics for first-passage percolation on subsets of $\mathbb{Z}^{2}$
It is an open problem to show that in two-dimensional first-passage percolation, the sequence of finite geodesics from any point to $(n,0)$ has a limit in $n$. In this paper, we consider this question for first-passage percolation on a wide class of subgraphs of $\mathbb{Z}^{2}$: those whose vertex set is …