ISRN Discrete Mathematics
Volume 2012 (2012), Article ID 758721, 6 pages
Uniqueness of the Infinite Component for Percolation on a Hierarchical Lattice
Institute for Cyber Security, University of Texas at San Antonio, San Antonio, TX 78249, USA
Received 5 July 2012; Accepted 16 August 2012
Academic Editors: U. A. Rozikov and X. Yong
Copyright © 2012 Yilun Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study a long-range percolation in the hierarchical lattice of order where probability of connection between two nodes separated by distance is of the form min, and . We show the uniqueness of the infinite component for this model.