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Consider the following forest fire model where the possible locations oftrees are the sites of $\mathbb{Z}$. Each site has three possible states:'vacant', 'occupied' or 'burning'. Vacant sites become occupied at rate $1$. Ateach site, ignition (by lightning) occurs at rate $\lambda$. When a site isignited, a fire starts and propagates to neighbors at rate $\pi$. We study theasymptotic behavior of this process as $\lambda\to0$ and $\pi\to\infty$. Weshow that there are three possible classes of scaling limits, according to theregime in which $\lambda\to0$ and $\pi\to\infty$.

Asymptotics of one dimensional forest fire process with non instantaneous propagation