Law of large numbers for the maximal flow through a domain of ${\mathbb{R}}^d$ in first passage percolation

Raphaël Cerf, Marie Théret

We consider the standard first passage percolation model in the rescaled graph ${\mathbb{Z}}^d/n$ for $d\ge 2$, and a domain $\Omega$ of boundary $\Gamma$ in ${\mathbb{R}}^d$. Let ${\Gamma }^1$ and $Γ^…