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Percolation Times in Two-Dimensional Models For Excitable Media

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Percolation Times in Two-Dimensional Models For Excitable Media
2.	Creator	Author's name, affiliation, country	Janko Gravner; University of California, Davis
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	additive growth dynamics, excitable media, Greenberg--Hastings model, percolation.
3.	Subject	Subject classification	60K35
4.	Description	Abstract	The three-color Greenberg--Hastings model (GHM) is a simple cellular automaton model for an excitable medium. Each site on the lattice $Z^2$ is initially assigned one of the states 0, 1 or 2. At each tick of a discrete--time clock, the configuration changes according to the following synchronous rule: changes $1\to 2$ and $2\to 0$ are automatic, while an $x$ in state 0 may either stay in the same state or change to 1, the latter possibility occurring iff there is at least one representative of state 1 in the local neighborhood of $x$. Starting from a product measure with just 1's and 0's such dynamics quickly die out (turn into 0's), but not before 1's manage to form infinite connected sets. A very precise description of this ``transient percolation'' phenomenon can be obtained when the neighborhood of $x$ consists of 8 nearest points, the case first investigated by S. Fraser and R. Kapral. In addition, first percolation times for related monotone models are addressed.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1996-10-10
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/12
10.	Identifier	Digital Object Identifier	10.1214/EJP.v1-12
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 1
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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