The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2307–2321 | Cite as

Recent advances and open challenges in percolation

Review
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications

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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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Departamento de Física, Faculdade de Ciências, Universidade de LisboaLisboaPortugal
  2. 2.Centro de Física Teórica e Computacional, Universidade de LisboaLisboaPortugal
  3. 3.JSC, FZ JülichJülichGermany
  4. 4.Department of Physics and AstronomySeoul National UniversitySeoulKorea
  5. 5.Computational Physics for Engineering Materials, IfB, ETH ZurichZurichSwitzerland
  6. 6.Department of ChemistryUniversity of CambridgeCambridgeUK
  7. 7.Center for the Study of Complex Systems and Department of Chemical Engineering, University of MichiganAnn ArborUSA

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