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arXiv · 1401.7130

Absence of infinite cluster for critical Bernoulli percolation on slabs

Hugo Duminil-Copin·Vladas Sidoravicius·Vincent Tassion
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Abstract

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

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Hugo Duminil-Copin, Vladas Sidoravicius, Vincent Tassion. 2014-01-28. Absence of infinite cluster for critical Bernoulli percolation on slabs. https://arxiv.org/abs/1401.7130

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