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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).
|Number of pages||41|
|Journal||Random Structures and Algorithms|
|Early online date||15 Dec 2017|
|Publication status||E-pub ahead of print - 15 Dec 2017|
- bootstrap percolation
- critical phenomena
- preferential attachment graphs
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- 1 Finished
Inhomogeneity and generalised bootstrap percolation in stochastic networks
Engineering & Physical Science Research Council
1/09/13 → 31/08/15
Project: Research Councils