Uniqueness of the Infinite Component for Percolation on a Hierarchical Lattice. (11th September 2012) - Shang, Yilun
Abstract : We study a long-range percolation in the hierarchical lattice Ω N of order N where probability of connection between two nodes separated by distance k is of the form min α β − k, 1 , α ≥ 0 and β > 0 . We show the uniqueness of the infinite component for this model.