Explosive Percolation in Random Networks

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Springer, Jul 15, 2014 - Mathematics - 63 pages

This thesis is devoted to the study of the Bohman-Frieze-Wormald percolation model, which exhibits a discontinuous transition at the critical threshold, while the phase transitions in random networks are originally considered to be robust continuous phase transitions. The underlying mechanism that leads to the discontinuous transition in this model is carefully analyzed and many interesting critical behaviors, including multiple giant components, multiple phase transitions, and unstable giant components are revealed. These findings should also be valuable with regard to applications in other disciplines such as physics, chemistry and biology.

 

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Contents

1 Introduction
1
2 Discontinuous Explosive Percolation with Multiple Giant Components
9
3 Deriving an Underlying Mechanism for Discontinuous Percolation Transitions
17
4 Continuous Phase Transitions in Supercritical Explosive Percolation
28
5 Unstable Supercritical Discontinuous Percolation Transitions
47
Appendix AAlgorithm of Percolation Models
61
Index
63
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