Invariant splitting of a slab into infinitely many robust clusters

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 ${\mathbb{Z}}^2$.

12 pages 8 figures