Competition between growths governed by Bernoulli Percolation

Olivier Garet (1) , Régine Marchand (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Percolation; first-passage percolation; chemical distance; competition; random growth

Domaines: Probabilités [math.PR]

Olivier Garet, Régine Marchand. Competition between growths governed by Bernoulli Percolation. Markov Processes And Related Fields, 2006, 12 (4), pp.695-734. ⟨hal-00005783⟩