PERCOLATION IN A VORONOI COMPETITION-GROWTH MODEL

We study a model in which two entities (e.g., plant species, political ideas,...) compete for space on a plane, starting from randomly distr ibuted seeds and growing deterministically at possibly different rates . An entity which forms an infinite cluster is considered to dominate over the other (which then cannot percolate). We analyze the occurrenc e of such a form of domination in situations in which one entity start s from a much larger density of seeds than the other one, but the latt er one grows at a much faster rate than the former one. The model stud ied here generalizes the problem of Voronoi percolation.