Long-range last-passage percolation on the line
Long-range last-passage percolation on the line
We consider directed last-passage percolation on the random graph $G=(V,E)$ where $V=\mathbb{Z}$ and each edge $(i,j)$, for $i<j\in\mathbb{Z}$, is present in $E$ independently with some probability $p\in (0,1]$. To every $(i,j)\in E$ we attach i.i.d. random weights $v_{i,j}>0$. We are interested in the behaviour of $w_{0,n}$, which is the maximum …