Contact process with destruction of cubes and hyperplanes

Forest fires versus tornadoes

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)352-365
Number of pages14
JournalJournal of Applied Probability
Volume48
Issue number2
DOIs
StatePublished - Jun 2011

Fingerprint

Forest Fire
Contact Process
Hyperplane
Regular hexahedron
Catastrophe
Survival Probability
Random number
Spatial Model
Hypergraph
Invariant Measure
Monotonic
Extinction
Stochastic Model
Model-based
Subset
Graph in graph theory
Range of data
Forest fire
Model

Keywords

  • Catastrophe
  • Contact process
  • Forest fire
  • Hypergraph
  • Tornado

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Contact process with destruction of cubes and hyperplanes : Forest fires versus tornadoes. / Lanchier, Nicolas.

In: Journal of Applied Probability, Vol. 48, No. 2, 06.2011, p. 352-365.

Research output: Contribution to journalArticle

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