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arXiv · 2401.16357

Invariant splitting of a slab into infinitely many robust clusters

Péter Mester
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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 $\mathbb{Z}^2$.

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Péter Mester. 2024-01-29. Invariant splitting of a slab into infinitely many robust clusters. https://arxiv.org/abs/2401.16357

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