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Continuous first-passage percolation and continuous greedy paths model : linear growth

Abstract : We study a random growth model on ${\Bbb R}^{d}$ introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim to find conditions on the distribution of the random radii to determine whether the growth of the process is linear or not. To do so, we compare this model with a continuous analogue of the greedy lattice paths model and transpose results for greedy paths from the lattice setting to the continuous setting.
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https://hal.archives-ouvertes.fr/hal-01159058
Contributor : Iecl Bibliothèque <>
Submitted on : Tuesday, June 2, 2015 - 3:05:16 PM
Last modification on : Monday, February 18, 2019 - 7:52:10 PM

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Jean-Baptiste Gouéré, Régine Marchand. Continuous first-passage percolation and continuous greedy paths model : linear growth. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2008, 18 (6), pp.2300-2319. ⟨10.1214/08-AAP52⟩. ⟨hal-01159058⟩

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