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

   
@article{ECP1229,
	author = {Maximilian Duerre},
	title = {Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {11},
	year = {2006},
	keywords = {forest-fires; self-organized criticality; forest-fire model; unique; adapted},
	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},
	pages = {no. 31, 304-315},
	issn = {1083-589X},
	doi = {10.1214/ECP.v11-1229},    
        url = {http://ecp.ejpecp.org/article/view/1229}}