English

Absence of infinite cluster for critical Bernoulli percolation on slabs

Probability 2014-01-29 v1 Mathematical Physics math.MP

Abstract

We prove that for Bernoulli percolation on a graph Z2×{0,,k}\mathbb{Z}^2\times\{0,\dots,k\} (k0k\ge 0), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on Z2\mathbb{Z}^2 which are invariant under π/2\pi/2-rotation and reflection.

Keywords

Cite

@article{arxiv.1401.7130,
  title  = {Absence of infinite cluster for critical Bernoulli percolation on slabs},
  author = {Hugo Duminil-Copin and Vladas Sidoravicius and Vincent Tassion},
  journal= {arXiv preprint arXiv:1401.7130},
  year   = {2014}
}

Comments

17 pages, 5 figures