Recent advances and open challenges in percolation

Abstract

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.

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Cited by in corpus (9)

• Recent advances in percolation theory and its applications
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Diverse types of percolation transitions
• Universality and Asymptotic Scaling in Drilling Percolation
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• From explosive to infinite-order transitions on a hyperbolic network
• Inverting the Achlioptas rule for explosive percolation
• Colored Percolation
• Variation of the critical percolation threshold in the Achlioptas processes