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Abstract
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or susceptible. At each round every susceptible vertex which has at least r > 1 infected neighbours becomes infected and remains so forever.
Assume that initially a(t) vertices are randomly infected, where t is the total number of vertices of the graph. Suppose also that r < m, where 2m is the average degree. We determine a critical function a_c(t) such that when
a(t) >> a_c(t), complete infection occurs with high probability as t goes to infinity, but when a(t) << a_c (t), then with high probability the process evolves only for a bounded number of rounds and the final set of infected vertices is asymptotically equal to a(t).
Original language  English 

Number of pages  41 
Journal  Random Structures and Algorithms 
Early online date  15 Dec 2017 
DOIs  
Publication status  Epub ahead of print  15 Dec 2017 
Keywords
 bootstrap percolation
 critical phenomena
 preferential attachment graphs
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Dive into the research topics of 'A phase transition in the evolution of bootstrap percolation processes on preferential attachment graphs'. Together they form a unique fingerprint.Projects
 1 Finished

Inhomogeneity and generalised bootstrap percolation in stochastic networks
Engineering & Physical Science Research Council
1/09/13 → 31/08/15
Project: Research Councils