Presentation of the model: we consider the regular lattice created from $\mathbb{Z}^d$.
- At $t=0$, each site is said "active" independently with a probability $p$, "inactive" otherwise.
- At $t$, if a site is inactive, it becomes active if at least $k$ of its neighbours are active.
We call neighbour of $x$ each element of $V(x)=\{y\in\mathbb{Z}^d, ||x-y||=1\}$. We note $S_t$ the set of the active sites
I'm studying the bootstrap percolation model on the $\Bbb Z^d$ lattice, and I wonder whether or not it is possible to calculate the average time for a $n\times n$ matrix to fill up (considering only matrices that can fill up).