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Nonmonotonic Coexistence Regions for the Two-Type Richardson Model on Graphs

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Nonmonotonic Coexistence Regions for the Two-Type Richardson Model on Graphs
2.	Creator	Author's name, affiliation, country	Maria Deijfen; Stockholm University, Sweden
2.	Creator	Author's name, affiliation, country	Olle Haggstrom; Chalmers University of Technology, Sweden
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Competing growth; graphs; coexistence
3.	Subject	Subject classification	60K35;82B43
4.	Description	Abstract	In the two-type Richardson model on a graph $G=(V,E)$, each vertex is at a given time in state $0$, $1$ or $2$. A $0$ flips to a $1$ (resp.\ $2$) at rate $\lambda_1$ ($\lambda_2$) times the number of neighboring $1$'s ($2$'s), while $1$'s and $2$'s never flip. When $G$ is infinite, the main question is whether, starting from a single $1$ and a single $2$, with positive probability we will see both types of infection reach infinitely many sites. This has previously been studied on the $d$-dimensional cubic lattice $Z^d$, $d\geq 2$, where the conjecture (on which a good deal of progress has been made) is that such coexistence has positive probability if and only if $\lambda_1=\lambda_2$. In the present paper examples are given of other graphs where the set of points in the parameter space which admit such coexistence has a more surprising form. In particular, there exist graphs exhibiting coexistence at some value of $\frac{\lambda_1}{\lambda_2} \neq 1$ and non-coexistence when this ratio is brought closer to $1$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2006-05-08
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/321
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-321
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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