An oriented competition model on .
Lalley, Steven P., Kordzakhia, George (2008)
Electronic Communications in Probability [electronic only]
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Lalley, Steven P., Kordzakhia, George (2008)
Electronic Communications in Probability [electronic only]
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Angel, Omer, Holroyd, Alexander E., Martin, James B. (2005)
Electronic Communications in Probability [electronic only]
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Kesten, Harry (1996)
Electronic Communications in Probability [electronic only]
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Boivin, Daniel, Derrien, Jean-Marc (2002)
Electronic Communications in Probability [electronic only]
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Janson, Svante (2009)
Electronic Journal of Probability [electronic only]
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Olivier Garet, Régine Marchand (2004)
ESAIM: Probability and Statistics
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The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on 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 vertices to a deterministic shape that does not depend on the realization of the infinite cluster. As a special case of our result, we obtain an asymptotic shape theorem for the chemical distance...
C. M. Newman, D. L. Stein (1995)
Annales de l'I.H.P. Probabilités et statistiques
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Kesten, H., Sidoravicius, V., Zhang, Y. (1998)
Electronic Journal of Probability [electronic only]
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Häggström, Olle, Jonasson, Johan (2006)
Probability Surveys [electronic only]
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Wästlund, Johan (2008)
Electronic Communications in Probability [electronic only]
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Deijfen, Maria, Jonasson, Johan (2006)
Electronic Communications in Probability [electronic only]
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