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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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Official URL: http://dx.doi.org/10.1016/j.spa.2015.08.005

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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
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:
DateEvent
January 2016Published
31 August 2015Available
22 August 2015Accepted
3 December 2014Submitted
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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