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Coexistence in a two-type continuum growth model

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  01 July 2016

Maria Deijfen  and
Olle Häggström
Maria Deijfen*
Affiliation:
Stockholm University
Olle Häggström*
Affiliation:
Chalmers University of Technology
*
∗ Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: mia@matematik.su.se
∗∗ Postal address: Department of Mathematical Statistics, Chalmers University of Technology, SE-412 91 Göteborg, Sweden. Email address: olleh@math.chalmers.se
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Abstract

We consider a stochastic model describing the growth of two competing infections on ℝd. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type-1 or -2 infected region causing all previously uninfected points within a stochastic distance from the outburst location to become type-1 or -2 infected, respectively. The main result is that, if the infection types have the same intensity, then there is a strictly positive probability that both infection types grow unboundedly.

Keywords

Richardson's modelcompeting growthcoexistence

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 36 , Issue 4 , December 2004 , pp. 973 - 980
Copyright
Copyright © Applied Probability Trust 2004 

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References

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