English

Bernoulli Hyperplane Percolation

Probability 2020-07-13 v1

Abstract

We study a dependent site percolation model on the nn-dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We extend the results about Bernoulli line percolation showing that the model undergoes a non-trivial phase transition and proving the existence of a transition from exponential to power-law decay within some regions of the subcritical phase.

Keywords

Cite

@article{arxiv.2007.05115,
  title  = {Bernoulli Hyperplane Percolation},
  author = {Marco Aymone and Marcelo R. Hilário and Bernardo N. B. de Lima and Vladas Sidoravicius},
  journal= {arXiv preprint arXiv:2007.05115},
  year   = {2020}
}

Comments

28 pages

R2 v1 2026-06-23T17:00:08.909Z