Uniqueness of the Infinite Component for Percolation on a Hierarchical Lattice

الملخص EN

We study a long-range percolation in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k,1}, α≥0 and β>0.

We show the uniqueness of the infinite component for this model.