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 Electronic Communications in Probability > Vol. 11 (2006) > Paper 31 open journal systems 


Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models

Maximilian Duerre,


Abstract
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


Full text: PDF

Pages: 304-315

Published on: December 10, 2006
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Electronic Communications in Probability. ISSN: 1083-589X