A stochastic model for competing growth on Rd

Deijfen, M. and Haggstrom, O. and Bagley, J. (2004) A stochastic model for competing growth on Rd. Markov Processes and Related Fields, 10 (2). pp. 217-248. ISSN 1024-2953

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Abstract

A stochastic model, describing the growth of two competing infections on Rd, is introduced. The growth is driven by outbursts in the infected region, an outburst in the type 1 (2) infected region transmitting the type 1 (2) infection to the previously uninfected parts of a ball with stochastic radius around the outburst point. The main result is that with the growth rate for one of the infection types ¯xed, mutual unbounded growth has probability zero for all but at most countably many values of the other infection rate. This is a continuum analog of a result of HÄaggstrÄom and Pemantle. We also extend a shape theorem of Deijfen for the correspond- ing model with just one type of infection.

Item Type: Article
Uncontrolled Keywords: Spatial spread, Richardson's model, shape theorem, competing growth
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 82 Statistical mechanics, structure of matter
Depositing User: Ms Lucy van Russelt
Date Deposited: 18 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/565

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