A stochastic model for competing growth on R^d [article]

Maria Deijfen, Olle Häggström, Jonathan Bagley
2015 arXiv   pre-print
A stochastic model, describing the growth of two competing infections on R^d, 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 fixed, mutual unbounded growth has probability zero for all but at most countably many values
more » ... of the other infection rate. This is a continuum analog of a result of Häggström and Pemantle. We also extend a shape theorem of Deijfen for the corresponding model with just one type of infection.
arXiv:1509.06961v1 fatcat:kmctu2mtcng4hglcjh4opybpbe