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Seven-dimensional forest fires

Annales de l'institut Henri Poincare (B) Probability and Statistics (2015) 51(3) 862-866
DOI: 10.1214/13-AIHP587
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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.

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Ahlberg, D., Duminil-Copin, H., Kozma, G., & Sidoravicius, V. (2015). Seven-dimensional forest fires. Annales de l’institut Henri Poincare (B) Probability and Statistics, 51(3), 862–866. https://doi.org/10.1214/13-AIHP587

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