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

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00161233
Contributor : Regine Marchand <>
Submitted on : Tuesday, July 10, 2007 - 11:39:18 AM
Last modification on : Friday, July 9, 2021 - 11:30:51 AM
Long-term archiving on: : Thursday, April 8, 2010 - 10:48:34 PM

### Files

ppp-D-unbounded.pdf
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### Identifiers

• HAL Id : hal-00161233, version 1
• ARXIV : 0707.1395

### Citation

Jean-Baptiste Gouere, Regine Marchand. Continuous first-passage percolation and continuous greedy paths model: linear growth. 2007. ⟨hal-00161233⟩

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