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2006 Existence of multi-dimensional infinite volume self-organized critical forest-fire models
Duerre Maximilian
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Electron. J. Probab. 11: 513-539 (2006). DOI: 10.1214/EJP.v11-333

Abstract

Consider the following forest-fire model where the possible locations of trees are the sites of a cubic lattice. Each site has two possible states: 'vacant' or 'occupied'. Vacant sites become occupied according to independent rate 1 Poisson processes. Independently, at each site ignition (by lightning) occurs according to independent rate lambda Poisson processes. When a site is ignited, its occupied cluster becomes vacant instantaneously. If the lattice is one-dimensional or finite, then with probability one, at each time the state of a given site only depends on finitely many Poisson events; a process with the above description can be constructed in a standard way. If the lattice is infinite and multi-dimensional, in principle, the state of a given site can be influenced by infinitely many Poisson events in finite time.

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Duerre Maximilian. "Existence of multi-dimensional infinite volume self-organized critical forest-fire models." Electron. J. Probab. 11 513 - 539, 2006. https://doi.org/10.1214/EJP.v11-333

Information

Accepted: 16 July 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1109.60081
MathSciNet: MR2242654
Digital Object Identifier: 10.1214/EJP.v11-333

Subjects:
Primary: 60K35
Secondary: 82C20 , 82C22

Keywords: existence , forest-fire model , forest-fires , Self-organized criticality , well-defined

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