Competition between growths governed by Bernoulli Percolation

Olivier Garet, Régine Marchand

Published 2005-07-07Version 1

We study a competition model on $\mathbb{Z}^d$ where the two infections are driven by supercritical Bernoulli percolations with distinct parameters $p$ and $q$. We prove that, for any $q$, there exist at most countably many values of $p<\min(q, \overrightarrow{p\_c})$ such that coexistence can occur.