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June 2011 Contact process with destruction of cubes and hyperplanes: forest fires versus tornadoes
N. Lanchier
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J. Appl. Probab. 48(2): 352-365 (June 2011). DOI: 10.1239/jap/1308662632


Nonspatial stochastic models of populations subject to catastrophic events result in the common conclusion that the survival probability of the population is nondecreasing with respect to the random number of individuals removed at each catastrophe. The purpose of this paper is to prove that such a monotonic relationship is not true for simple spatial models based on Harris' contact processes, whose dynamics are described by hypergraph structures rather than traditional graph structures. More precisely, it is proved that, for a wide range of parameters, the destruction of (infinite) hyperplanes does not affect the existence of a nontrivial invariant measure, whereas the destruction of large (finite) cubes drives the population to extinction, a result that we depict by using the biological picture: forest fires are more devastating than tornadoes. This indicates that the geometry of the subsets struck by catastrophes is somewhat more important than their area, thus the need to consider spatial rather than nonspatial models in this context.


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N. Lanchier. "Contact process with destruction of cubes and hyperplanes: forest fires versus tornadoes." J. Appl. Probab. 48 (2) 352 - 365, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1219.60086
MathSciNet: MR2840304
Digital Object Identifier: 10.1239/jap/1308662632

Primary: 60K35

Keywords: catastrophe , contact process , forest fire , Hypergraph , tornado

Rights: Copyright © 2011 Applied Probability Trust


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Vol.48 • No. 2 • June 2011
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