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A forest-fire model on the upper half-plane

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1.	Title	Title of document	A forest-fire model on the upper half-plane
2.	Creator	Author's name, affiliation, country	Robert Graf; Ludwig Maximilian University; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	forest-fire model, upper half-plane, self-organized criticality, phase transition
3.	Subject	Subject classification	60K35; 82C22; 82B43
4.	Description	Abstract	We consider a discrete forest-fire model on the upper half-plane of the two-dimensional square lattice. Each site can have one of the following two states: "vacant" or "occupied by a tree". At the starting time all sites are vacant. Then the process is governed by the following random dynamics: Trees grow at rate 1, independently for all sites. If an occupied cluster reaches the boundary of the upper half plane or if it is about to become infinite, the cluster is instantaneously destroyed, i.e. all of its sites turn vacant. Additionally, we demand that the model is invariant under translations along the x-axis. We prove that such a model exists and arises naturally as a subseqential limit of forest-fire processes in finite boxes when the box size tends to infinity. Moreover, the model exhibits a phase transition in the following sense: There exists a critical time $t_c$ (which corresponds with the critical probability $p_c$ in ordinary site percolation by $1 - e^{-t_c} = p_c$) such that before $t_c$, only sites close to the boundary have been affected by destruction, whereas after $t_c$, sites on the entire half-plane have been affected by destruction.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Studienstiftung des deutschen Volkes
7.	Date	(YYYY-MM-DD)	2014-01-13
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2625
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2625
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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