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Shape of territories in some competing growth models

Jean-Baptiste Gouéré
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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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Jean-Baptiste Gouéré. 2007-10-23. Shape of territories in some competing growth models. https://doi.org/10.1214/105051607000000113

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