Seven-dimensional forest fires
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 862-866.

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.

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.

DOI : https://doi.org/10.1214/13-AIHP587
Mots clés : near-critical percolation, static renormalization
@article{AIHPB_2015__51_3_862_0,
     author = {Ahlberg, Daniel and Duminil-Copin, Hugo and Kozma, Gady and Sidoravicius, Vladas},
     title = {Seven-dimensional forest fires},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {862--866},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {3},
     year = {2015},
     doi = {10.1214/13-AIHP587},
     zbl = {1323.60123},
     mrnumber = {3365964},
     language = {en},
     url = {archive.numdam.org/item/AIHPB_2015__51_3_862_0/}
}
Ahlberg, Daniel; Duminil-Copin, Hugo; Kozma, Gady; Sidoravicius, Vladas. Seven-dimensional forest fires. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 862-866. doi : 10.1214/13-AIHP587. http://archive.numdam.org/item/AIHPB_2015__51_3_862_0/

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