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Generalizations of forest fires with ignition at the origin

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium) Special processes

Published online by Cambridge University Press:  24 October 2022

Francis Comets ,
Mikhail Menshikov  and
Stanislav Volkov Open the ORCID record for Stanislav Volkov [Opens in a new window]
Francis Comets
Affiliation:
Université de Paris
Mikhail Menshikov*
Affiliation:
Durham University
Stanislav Volkov*
Affiliation:
Lund University
*
*Postal address: Department of Mathematical Sciences, Durham University, DH1 3LE, UK. Email address: mikhail.menshikov@durham.ac.uk
**Postal address: Centre for Mathematical Sciences, Lund University, SE-22100, Sweden. Email address: stanislav.volkov@matstat.lu.se
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Abstract

We study generalizations of the forest fire model introduced in [4] and [10] by allowing the rates at which the trees grow to depend on their location, introducing long-range burning, as well as a continuous-space generalization of the model. We establish that in all the models in consideration the expected time required to reach a site at distance x from the origin is of order $(\!\log x)^{(\!\log 2)^{-1}+\delta}$ for any $\delta>0$ .

Keywords

Forest fire modellong-range interactionstime-dependent percolationself-organized criticality

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82C43: Time-dependent percolation 92D25: Population dynamics (general)
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 2 , June 2023 , pp. 418 - 434
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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