Monotonicity of Percolation Probability on ${\mathbb{Z}}^d$ with Long Range Connections

Bernardo N. B. de Lima, Rémy Sanchis, Roger W. C. Silva

Consider an independent site percolation model on ${\mathbb{Z}}^d,d\ge 2$, with parameter $p\in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ par…