In a one-dimensional forest fire model with random delays, almost surely some fire never stops (an 'infinite fire'), with a phase transition at delays decaying like c/x with c=1.
Generalizations of forest fires with ignition at the origin
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Forest Fire Model on $\mathbb{Z}_{+}$ with Delays
In a one-dimensional forest fire model with random delays, almost surely some fire never stops (an 'infinite fire'), with a phase transition at delays decaying like c/x with c=1.