Invariant splitting of a slab into infinitely many robust clusters

Péter Mester

Invariant splitting of a slab into infinitely many robust clusters

Probability 2024-01-30 v1

Authors: Péter Mester

Abstract

We give an example of an invariant bond percolation process on the slab $\mathbb{Z}^2\times \{0,1\}$ with the property that it has infinitely many clusters whose critical percolation probability is strictly less than $1$ . We also show that no such process can exist in $\mathbb{Z}^2$ .

Keywords

invariant bond percolation slab robust clusters critical percolation probability infinitely many clusters

Cite

@article{arxiv.2401.16357,
  title  = {Invariant splitting of a slab into infinitely many robust clusters},
  author = {Péter Mester},
  journal= {arXiv preprint arXiv:2401.16357},
  year   = {2024}
}

Comments

12 pages 8 figures

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