Explosive Percolation in Random Networks

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.

Nominated as an outstanding Ph.D. thesis by Peking University, Beijing, China The first to discover multiple giant components in a discontinuous percolation transition of random networks for the first time Presents the first discovery of hybrid of both continuous and discontinuous percolation transition in a networked system Reveals multiple giant components emerging in a percolation transition of a networked system Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- Discontinuous Explosive Percolation with Multiple Giant Components.- Deriving An Underlying Mechanism for Discontinuous Percolation Transitions.- Continuous Phase Transitions in Supercritical Explosive Percolation.- Unstable Supercritical Discontinuous Percolation Transitions.- Algorithm of percolation models.