Forest Fire Model on ${\mathbb{Z}}_{+}$ with Delays

Abstract

We consider a generalization of the forest fire model on ${\mathbb{Z}}_{+}$ with ignition at zero only, studied in [arXiv:0907.1821]. Unlike that model, we allow delays in the spread of the fires as well as the non-zero burning time of individual ``trees''. We obtain some general properties for this model, which cover, among others, the phenomena of an ``infinite fire'', not present in the original model.