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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