We consider Bernoulli bond percolation on the product graph of a regular tree and a line. We show that the triangle condition does not hold at the uniqueness threshold.
Critical probability on the product graph of a regular tree and a line
On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime
Percolation at the uniqueness threshold via subgroup relativization
![QR code for arXiv:1811.01477 [math.PR]](http://oss.arxitics.com/images/favicon.svg)