Generalizations of forest fires with ignition at the origin

Francis Comets; Mikhail Menshikov; Stanislav Volkov

doi:10.1017/jpr.2022.51

Generalizations of forest fires with ignition at the origin

Francis Comets, Mikhail Menshikov, Stanislav Volkov

Mathematical Statistics

Research output: Contribution to journal › Article › peer-review

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 for any 0$ ]]>.

Original language	English
Pages (from-to)	418-434
Number of pages	17
Journal	Journal of Applied Probability
Volume	60
Issue number	2
DOIs	https://doi.org/10.1017/jpr.2022.51
Publication status	Published - 2023

Subject classification (UKÄ)

Physical Geography
Probability Theory and Statistics

Free keywords

Forest fire model
long-range interactions
self-organized criticality
time-dependent percolation

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10.1017/jpr.2022.51

Cite this

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title = "Generalizations of forest fires with ignition at the origin",

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 for any 0$ ]]>.",

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AB - 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 for any 0$ ]]>.

KW - Forest fire model

KW - long-range interactions

KW - self-organized criticality

KW - time-dependent percolation

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DO - 10.1017/jpr.2022.51

M3 - Article

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SP - 418

EP - 434

JO - Journal of Applied Probability

JF - Journal of Applied Probability

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ER -

Generalizations of forest fires with ignition at the origin

Abstract

Subject classification (UKÄ)

Free keywords

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Cite this