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Pré-Publication, Document De Travail Année : 2021

Generalizations of forest fires with ignition at origin

Mikhail Menshikov
  • Fonction : Auteur
Stanislav Volkov
  • Fonction : Auteur

Résumé

We study generalizations of the Forest Fire model introduced in~\cite{BTRB} and~\cite{Volk} 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 $(\log x)^{(\log 2)^{-1}+\delta}$ for any $\delta>0$.

Dates et versions

hal-03180348 , version 1 (24-03-2021)

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Francis Comets, Mikhail Menshikov, Stanislav Volkov. Generalizations of forest fires with ignition at origin. 2021. ⟨hal-03180348⟩
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