arXiv subjects
Publications and source records attributed to Rodrigo G. Couto.
We consider anisotropic independent bond percolation models on the slab $\Z^2\times\{0,\dots,k\}$, where we suppose that the axial (vertical) bonds are open with probability $p$, while the radial (horizontal) bonds are open with probability $q$. We study the critical curves for these models and establish their continuity and strict monotonicity.
We consider an anisotropic bond percolation model on $\mathbb{Z}^2$, with $\textbf{p}=(p_h,p_v)\in [0,1]^2$, $p_v>p_h$, and declare each horizontal (respectively vertical) edge of $\mathbb{Z}^2$ to be open with probability $p_h$(respectively $p_v$), and otherwise closed, independently of all other edges. Let $x=(x_1,x_2) \in \mathbb{Z}^2$ with $0 \prob(\{0\leftrightarrow x'\})$. In this note we give an affirmative answer in the highly supercritical regime.