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