Shape of territories in some competing growth models
Jean-Baptiste Gouéré
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 i infection, it remains of type i forever. We give results about the shape of the area ultimately infected by the different infections.
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