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Article Dans Une Revue The Annals of Applied Probability Année : 2005

Coexistence in two-type first-passage percolation models

Résumé

We study the problem of coexistence in a two-type competition model governedby first-passage percolation on $\Zd$ or on the infinite cluster in Bernoulli percolation.Actually, we prove for a large class of ergodic stationary passage times that for distinct points $x,y\in\Zd$, there is a strictly positive probability that$\{z\in\Zd;d(y,z)d(x,z)\}$ are both infinite sets.We also show that there is a strictly positive probability that the graph of time-minimizing path from the origin in first-passage percolation has at least two topological ends. This generalizes results obtained by H{ä}ggstr{ö}m and Pemantle forindependent exponential times on the square lattice.
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Dates et versions

hal-00000971 , version 1 (18-12-2003)

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Olivier Garet, Régine Marchand. Coexistence in two-type first-passage percolation models. The Annals of Applied Probability, 2005, 15, No. 1A, p. 298-330. ⟨10.1214/105051604000000503⟩. ⟨hal-00000971⟩
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