Explosive Percolation: Novel critical and supercritical phenomena

Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation transitions exhibit an array of novel universality classes and supercritical behaviors including a stochastic sequence of discontinuous transitions, multiple giant components, and lack of self-averaging. Many mechanisms that give rise to explosive percolation have been discovered, including overtaking, correlated percolation, and evolution on hierarchical lattices. Many connections to real-world systems, ranging from social networks to nanotubes, have been identified and explosive percolation is an emerging paradigm for modeling these systems as well as the consequences of small interventions intended to delay phase transitions. This review aims to synthesize existing results on explosive percolation and to identify fruitful directions for future research.