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

DOI10.1214/08-AAP523zbMath1154.60074arXiv0707.1395MaRDI QIDQ2378632

Jean-Baptiste Gouéré, Régine Marchand

Publication date: 13 January 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1395

zbMATH Keywords

first-passage percolationBoolean percolationrandom growthgreedy paths

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (6)

Multiple Phase Transitions in Long-Range First-Passage Percolation on Square Lattices ⋮ Spatial growth processes with long range dispersion: microscopics, mesoscopics and discrepancy in spread rate ⋮ Measure-valued growth processes in continuous space and growth properties starting from an infinite interface ⋮ The continuous-time frog model can spread arbitrarily fast ⋮ Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes ⋮ Continuity of the time constant in a continuous model of first passage percolation

Cites Work

• Subcritical regimes in the Poisson Boolean model of continuum percolation
• Greedy lattice animals. I: Upper bounds
• Greedy lattice animals. II: Linear growth
• Linear growth for greedy lattice animals.
• Shape of territories in some competing growth models
• Asymptotic shape in a continuum growth model
• Coexistence in a two-type continuum growth model
• A stochastic model for competing growth on $\mathbb{R}^d$

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