Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Seven-dimensional forest fires

Daniel Ahlberg, Hugo Duminil-Copin, Gady Kozma, and Vladas Sidoravicius

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We show that in high dimensional Bernoulli bond percolation, removing from a thin infinite cluster a much thinner infinite cluster leaves an infinite component. This observation has implications for the van den Berg–Brouwer forest fire process, also known as self-destructive percolation, for dimension high enough.


Cette article montre que dans la percolation de Bernoulli par arête en grande dimension, retirer d’une composante connexe infinie de faible densité une composante connexe de densité beaucoup plus faible laisse une composante connexe infinie. Cette observation a des implications pour le processus de feux de forêt de van den Berg–Brouwer, également connu sous le nom de percolation auto-destructive, en dimension suffisamment grande.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 862-866.

Received: 27 February 2013
Revised: 16 September 2013
Accepted: 22 September 2013
First available in Project Euclid: 1 July 2015

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Near-critical percolation Static renormalization


Ahlberg, Daniel; Duminil-Copin, Hugo; Kozma, Gady; Sidoravicius, Vladas. Seven-dimensional forest fires. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 862--866. doi:10.1214/13-AIHP587.

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