Competition between growths governed by Bernoulli Percolation

Details Competition between growths governed by Bernoulli Percolation Competition between growths governed by Bernoulli Percolation

2005-07-07

arxiv.org/abs/math/0507133v1

Markov Processes and Related Fields 12, 4 (01/12/2006) 695-734

Mathematics

Probability

30 pages with figures

Scientific paper

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.

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