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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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.

Résumé

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1435759231

Digital Object Identifier
doi:10.1214/13-AIHP587

Mathematical Reviews number (MathSciNet)
MR3365964

Zentralblatt MATH identifier
1323.60123

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

Keywords
Near-critical percolation Static renormalization

Citation

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. https://projecteuclid.org/euclid.aihp/1435759231


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