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The two-type Richardson model with unbounded initial configurations
Stockholm University, Faculty of Science, Department of Mathematics. Matematisk statistik.
2007 (English)In: Annals of Applied Probability, Vol. 17, no 5Article in journal (Refereed) Published
Abstract [en]

The two-type Richardson model describes the growth of two competing infections on Z^d and the main question is whether both infection types can simultaneously grow to occupy infinite parts of Z^d. For bounded initial configurations, this has been thoroughly studied. In this paper, an unbounded initial configuration consisting of points x=(x_1,...,x_d) in the hyperplane H={x in Z^d: x_1=0} is considered. It is shown that, starting from a configuration where all points in H\{0} are type 1 infected and the origin 0 is type 2 infected, there is a positive probability for the type 2 infection to grow unboundedly if and only if it has a strictly larger intensity than the type 1 infection. If instead the initial type 1 infection is restricted to the negative x_1-axis, it is shown that the type 2 infection at the origin can grow unboundedly also when the infection types have the same intensity.

Place, publisher, year, edition, pages
2007. Vol. 17, no 5
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-10199ISI: 000250270600008OAI: oai:DiVA.org:su-10199DiVA: diva2:176718
Available from: 2007-12-21 Created: 2007-12-21 Last updated: 2011-01-11Bibliographically approved

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