Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

Klaus Lichtenegger; Wilhelm Schappacher

doi:10.1142/s0129183109014321

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arXiv · 0902.3680

Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

Klaus Lichtenegger·Wilhelm Schappacher

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Abstract

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.

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Klaus Lichtenegger, Wilhelm Schappacher. 2009-02-23. Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood. https://doi.org/10.1142/s0129183109014321

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