Open Access
2006 Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models
Maximilian Duerre
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Electron. Commun. Probab. 11: 304-315 (2006). DOI: 10.1214/ECP.v11-1229


In a forest-fire model, each site of the square lattice is either vacant or occupied by a tree. Vacant sites get occupied according to independent rate 1 Poisson processes. Independently at each site ignition occurs according to independent rate lambda Poisson processes. When a site is hit by ignition, then its whole occupied cluster becomes vacant instantaneously. The article studies whether a multi-dimensional infinite volume forest-fire process with given parameter is unique. Under an assumption on the decay of the cluster size distribution, a process that dominates the forest-fire process is used to show uniqueness. If lambda is big enough, then subcritical site percolation shows the correctness of the assumption


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Maximilian Duerre. "Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models." Electron. Commun. Probab. 11 304 - 315, 2006.


Accepted: 10 December 2006; Published: 2006
First available in Project Euclid: 4 June 2016

zbMATH: 1130.60091
MathSciNet: MR2266720
Digital Object Identifier: 10.1214/ECP.v11-1229

Primary: 60K35
Secondary: 82C20 , 82C22

Keywords: adapted , forest-fire model , forest-fires , Self-organized criticality , unique

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