Coexistence in two-type first-passage percolation models

dc.creatorGaret, Olivier
dc.creatorMarchand, Regine
dc.date2003-12-18
dc.date.accessioned2026-07-07T06:31:53Z
dc.date.available2026-07-07T06:31:53Z
dc.descriptionWe study the problem of coexistence in a two-type competition model governed by 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 $\{z\in\Zd;d(y,z)<d(x,z)\}$ and $\{z\in\Zd;d(y,z)>d(x,z)\}$ 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 for independent exponential times on the square lattice.
dc.descriptionsubmitted 18 dec 2003
dc.identifierhttps://arxiv.org/abs/math/0312369
dc.identifierhttp://arxiv.org/abs/math/0312369
dc.identifierAnnals of Applied Probability 15, No. 1A (2005) pages 298-330
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98742
dc.subjectProbability
dc.subject60K35; 82B43
dc.titleCoexistence in two-type first-passage percolation models
dc.typetext

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