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August 2015 Seven-dimensional forest fires
Daniel Ahlberg, Hugo Duminil-Copin, Gady Kozma, Vladas Sidoravicius
Ann. Inst. H. Poincaré Probab. Statist. 51(3): 862-866 (August 2015). DOI: 10.1214/13-AIHP587

Abstract

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.

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Daniel Ahlberg. Hugo Duminil-Copin. Gady Kozma. Vladas Sidoravicius. "Seven-dimensional forest fires." Ann. Inst. H. Poincaré Probab. Statist. 51 (3) 862 - 866, August 2015. https://doi.org/10.1214/13-AIHP587

Information

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

zbMATH: 1323.60123
MathSciNet: MR3365964
Digital Object Identifier: 10.1214/13-AIHP587

Subjects:
Primary: 60K35

Rights: Copyright © 2015 Institut Henri Poincaré

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Vol.51 • No. 3 • August 2015
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