Weak shape theorem in first passage percolation with infinite passage times

Understand

We consider the model of i.i.d.

• first passage percolation on $\mathbb{Z}^d$ : we associate with each edge $e$ of the graph a passage time $t(e)$ taking values in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$.
• Equivalently, we consider a standard (finite) i.i.d.
• first passage percolation model on a super-critical Bernoulli percolation performed independently.