@article{EJP333,
author = {Duerre Maximilian},
title = {Existence of multi-dimensional infinite volume self-organized critical forest-fire models},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {forest-fires; self-organized criticality; forest-fire model; existence; well-defined},
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.},
pages = {no. 21, 513-539},
issn = {1083-6489},
doi = {10.1214/EJP.v11-333},
url = {http://ejp.ejpecp.org/article/view/333}}