A note on inhomogeneous percolation (Q1336565)

The independent bond percolation model on \(\mathbb{Z}^ 2\) with inhomogeneous probabilities \(p\{x, y\}\), \(x,y \in \mathbb{Z}^ 2\), of the \(\{x, y\}\)-bond opening is considered. The bonds with vertices in the \(X\) axis are open with probability \(\delta\) and all other bonds are open with probability \(p\). The author shows that no percolation occurs at \(p_ c\) for any \(\delta < 1\).