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

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

2007-07-10

arxiv.org/abs/0707.1395v1

Mathematics

Probability

13 pages, two appendices

Scientific paper

We study a random growth model on $\R^d$ 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 at finding 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 in the lattice setting to the continuous setting.

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