Explosive Percolation: Novel critical and supercritical phenomena

TL;DR

Explosive percolation describes a sudden transition to large-scale connectivity in networks, characterized by novel phenomena like multiple giant components and non-self-averaging, with applications across various real-world systems.

Contribution

This paper synthesizes existing research on explosive percolation, highlighting new universality classes, mechanisms, and potential applications, and suggests directions for future studies.

Findings

Identification of multiple giant components

Presence of non-self-averaging behavior

Discovery of various mechanisms like overtaking and correlated percolation

Abstract

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.