Open AccessUniqueness of the Infinite Component for Percolation on a Hierarchical Lattice
Author(s) -
Yilun Shang
Publication year - 2012
Publication title -
isrn discrete mathematics
Language(s) - English
Resource type - Journals
ISSN - 2090-7788
DOI - 10.5402/2012/758721
Subject(s) - uniqueness , lattice (music) , percolation threshold , mathematics , percolation (cognitive psychology) , percolation theory , statistical physics , component (thermodynamics) , combinatorics , mathematical analysis , topology (electrical circuits) , physics , quantum mechanics , electrical resistivity and conductivity , psychology , acoustics , neuroscience
We study a long-range percolation in the hierarchical lattice Ω of order where probability of connection between two nodes separated by distance is of the form min{−,1}, ≥0 and >0. We show the uniqueness of the infinite component for this model.
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