Shape of territories in some competing growth models
arXiv:math/0607226 · doi:10.1214/105051607000000113
Abstract
We study two competing growth models. Each of these models describes the spread of a finite number of infections on a graph. Each infection evolves like an (oriented or unoriented) first passage percolation process except that once a vertex is infected by type infection, it remains of type forever. We give results about the shape of the area ultimately infected by the different infections.
Published in at http://dx.doi.org/10.1214/105051607000000113 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)