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2006.345: A stochastic model for competing growth on Rd

2006.345: M. Deijfen, O. Haggstrom and J. Bagley (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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Official URL: http://www.math.msu.su/~malyshev/cont03.htm

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 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 82 Statistical mechanics, structure of matter
MIMS number:2006.345
Deposited By:Miss Louise Stait
Deposited On:18 August 2006

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