A remark on monotonicity in Bernoulli bond Percolation

Consider an anisotropic independent bond percolation model on the $d$-dimensional hypercubic lattice, $d\ge 2$, with parameter $p$. We show that the two point connectivity function $P_{p}({(0,\dots,0)\leftrightarrow (n,0,\dots,0)})$isamonotonefunctionin$n$whentheparameter$p$ is close enough to 0. Analogously, we show that truncated connectivity function $P_{p}({(0,\dots,0)\leftrightarrow (n,0,\dots,0), (0,\dots,0)\nleftrightarrow\infty})$isalsoamonotonefunctionin$n$when$p$ is close to 1.