Asymptotics of one-dimensional forest fire processes

DOI10.1214/09-AOP524zbMath1205.60167arXiv0812.1099OpenAlexW2084754207MaRDI QIDQ1958459

Nicolas Fournier, Xavier Bressaud

Publication date: 29 September 2010

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

Full work available at URL: https://arxiv.org/abs/0812.1099

zbMATH Keywords

self-organized criticalityPoisson processesstochastic interacting particle systemsforest fire modelcadlag paths

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Dynamic critical phenomena in statistical mechanics (82C27)

Related Items (3)

Self-destructive percolation as a limit of forest-fire models on regular rooted trees ⋮ Burning cars in a parking lot ⋮ Linear de-preferential urn models

Cites Work

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• Existence of multi-dimensional infinite volume self-organized critical forest-fire models
• Self-organized forest-fires near the critical time
• On the invariant distribution of a one-dimensional avalanche process
• On the asymptotic density in a one-dimensional self-organized critical forest-fire model
• Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models
• The cluster size distribution for a forest-fire process on \(\mathbb Z\)
• Self-organized criticality

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