Uniqueness of the Infinite Component for Percolation on a Hierarchical Lattice

Figure 1

An illustration of hierarchical lattice Ω₂ of order 2. The distances between three nodes 𝟎=(0,0,0,…), 𝐱=(1,0,0,…) and 𝐲=(0,1,0,…) are 𝑑(𝟎,𝐱)=1 and 𝑑(𝟎,𝐲)=𝑑(𝐱,𝐲)=2.