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An oriented competition model on $Z_+^2$

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	An oriented competition model on $Z_+^2$
2.	Creator	Author's name, affiliation, country	Steven P Lalley; University of Chicago
2.	Creator	Author's name, affiliation, country	George Kordzakhia; University of California, Berkeley
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	competition, shape theorem, first passage percolation
3.	Subject	Subject classification	60J25; 60K35
4.	Description	Abstract	We consider a two-type oriented competition model on the first quadrant of the two-dimensional integer lattice. Each vertex of the space may contain only one particle of either Red type or Blue type. A vertex flips to the color of a randomly chosen southwest nearest neighbor at exponential rate 2. At time zero there is one Red particle located at $(1,0)$ and one Blue particle located at $(0,1)$. The main result is a partial shape theorem: Denote by $R (t)$ and $B (t)$ the red and blue regions at time $t$. Then (i) eventually the upper half of the unit square contains no points of $B (t)/t$, and the lower half no points of $R (t)/t$; and (ii) with positive probability there are angular sectors rooted at $(1,1)$ that are eventually either red or blue. The second result is contingent on the uniform curvature of the boundary of the corresponding Richardson shape.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF Grant DMS-0405102
7.	Date	(YYYY-MM-DD)	2008-10-18
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1422
10.	Identifier	Digital Object Identifier	10.1214/ECP.v13-1422
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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