Uniqueness of the Infinite Component for Percolation on a Hierarchical Lattice. (11th September 2012)

• Record Type: Journal Article
• Authors: Shang, Yilun
• Other Names: Rozikov U. A. Academic Editor.; Yong X. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2012(2012)
• Publication Date: 2012-09-11
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2012/758721
• Languages: English
• ISSNs: 2090-7788

Abstract

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.