The Cluster Size Distribution for a Forest-Fire Process on $Z$
The Cluster Size Distribution for a Forest-Fire Process on $Z$
Consider the following forest-fire model where trees are located on sites of $\mathbb{Z}$. A site can be vacant or be occupied by a tree. Each vacant site becomes occupied at rate $1$, independently of the other sites. Each site is hit by lightning with rate $\lambda$, which burns down the …