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 i infection, it remains of type i forever. We give results about the shape of the area ultimately infected by the different infections.
"Shape of territories in some competing growth models." Ann. Appl. Probab. 17 (4) 1273 - 1305, August 2007. https://doi.org/10.1214/105051607000000113