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Competition between growths governed by Bernoulli Percolation

Olivier Garet·Régine Marchand
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Abstract

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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Olivier Garet, Régine Marchand. 2005-07-07. Competition between growths governed by Bernoulli Percolation. https://arxiv.org/abs/math/0507133

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