Generalizations of forest fires with ignition at origin

2019/10/01 by Francis Comets, Mikhail Menshikov, Comets, Francis +3
Mathematics · Physics and Astronomy · #60K35 #82C43 #92D25 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.1910.00212

openalex publication_date 2019/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study generalizations of the Forest Fire model introduced in [van den Berg, J., and Járai, A. A. "On the asymptotic density in a one-dimensional self-organized critical forest-fire model". Comm. Math. Phys. 253 (2005)] and [Volkov, Stanislav. "Forest fires on ℤ₊ with ignition only at 0". ALEA 6 (2009)] by allowing the rates at which the tree grow to depend on their location, introducing long-range burning, as well as continuous-space generalization of the model. We establish that in all the models in consideration the time required to reach site at distance x from the origin is of order at most (log x)^(log 2)^-1+δ for any δ>0.

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