Asymptotic shape for the chemical distance and first-passage percolation in random environment

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dc.creatorGaret, Olivier
dc.creatorMarchand, Regine
dc.date2003-04-11
dc.date.accessioned2026-07-07T06:31:53Z
dc.date.available2026-07-07T06:31:53Z
dc.descriptionThe aim of this paper is to generalize the well-known asymptotic shape result for first-passage percolation on $\Zd$ to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet points to a deterministic shape that does not depend on the random environment. As a special case of the previous result, we obtain an asymptotic shape theorem for the chemical distance in supercritical Bernoulli percolation. We also prove a flat edge result. Some various examples are also given.
dc.descriptionredaction du 10 avril 2003
dc.identifierhttps://arxiv.org/abs/math/0304144
dc.identifierhttp://arxiv.org/abs/math/0304144
dc.identifierESAIM: Probability and Statistics 8 (2004) pages 169-199
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98739
dc.subjectProbability
dc.subject60G15; 60K35; 82B43
dc.titleAsymptotic shape for the chemical distance and first-passage percolation in random environment
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