We study a random growth model on ℝd 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.
Publié le : 2008-12-15
Classification:
First-passage percolation,
greedy paths,
Boolean percolation,
random growth,
60K35,
82B43
@article{1227708919,
author = {Gou\'er\'e, Jean-Baptiste and Marchand, R\'egine},
title = {Continuous first-passage percolation and continuous greedy paths model: Linear growth},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 2300-2319},
language = {en},
url = {http://dml.mathdoc.fr/item/1227708919}
}
Gouéré, Jean-Baptiste; Marchand, Régine. Continuous first-passage percolation and continuous greedy paths model: Linear growth. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 2300-2319. http://gdmltest.u-ga.fr/item/1227708919/