The Annals of Applied Probability

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

Jean-Baptiste Gouéré and Régine Marchand

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2300-2319.

Dates
First available in Project Euclid: 26 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1227708919

Digital Object Identifier
doi:10.1214/08-AAP523

Mathematical Reviews number (MathSciNet)
MR2474537

Zentralblatt MATH identifier
1154.60074

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]

Keywords
First-passage percolation greedy paths Boolean percolation random growth

Citation

Gouéré, Jean-Baptiste; Marchand, Régine. Continuous first-passage percolation and continuous greedy paths model: Linear growth. Ann. Appl. Probab. 18 (2008), no. 6, 2300--2319. doi:10.1214/08-AAP523. https://projecteuclid.org/euclid.aoap/1227708919


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