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Bootstrap percolation and the geometry of complex networks
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Candellero, Elisabetta and Fountoulakis, Nikolaos (2016) Bootstrap percolation and the geometry of complex networks. Stochastic Processes and their Applications, 126 (1). pp. 234-264. doi:10.1016/j.spa.2015.08.005
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WRAP_1272725-st-260815-hyperbolic_graph_bootstrap_percolation.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (726Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.spa.2015.08.005
Abstract
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having N vertices, a dependent version of the Chung-Lu model. The process starts with infection rate p=p(N). Each uninfected vertex with at least View the MathML source infected neighbors becomes infected, remaining so forever. We identify a function pc(N)=o(1) such that a.a.s. when p≫pc(N) the infection spreads to a positive fraction of vertices, whereas when p≪pc(N) the process cannot evolve. Moreover, this behavior is “robust” under random deletions of edges.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Bootstrap (Statistics), Geometry, Hyperbolic, Random graphs, Mathematical analysis, Percolation (Statistical physics) | ||||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||
| Publisher: | Elsevier Science BV | ||||||||||
| ISSN: | 0304-4149 | ||||||||||
| Official Date: | January 2016 | ||||||||||
| Dates: |
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| Date of first compliant deposit: | 28 July 2016 | ||||||||||
| Volume: | 126 | ||||||||||
| Number: | 1 | ||||||||||
| Page Range: | pp. 234-264 | ||||||||||
| DOI: | 10.1016/j.spa.2015.08.005 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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