Shape of territories in some competing growth models

Details Shape of territories in some competing growth models Shape of territories in some competing growth models

2006-07-09

arxiv.org/abs/math/0607226v2

Annals of Applied Probability 2007, Vol. 17, No. 4, 1273-1305

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000113 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000113

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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