Monotonicity of the critical point in two-dimensional oriented percolation with enhancement

Abstract

In this note, we investigate Bernoulli oriented bond percolation with parameter $p$ on ${\mathbb{Z}}^2$. In addition to the standard edges, which are open with probability $p$, we introduce diagonal edges each open with probability $\epsilon$. Every edge is open or closed independently of all other edges. We prove that the critical parameter for this model is strictly decreasing in $\epsilon$.

References in corpus (1)

• A note on oriented percolation with inhomogeneities and strict inequalities