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Recent advances and open challenges in percolation

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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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Authors and Affiliations

  1. Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016, Lisboa, Portugal

    N. Araújo

  2. Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016, Lisboa, Portugal

    N. Araújo

  3. JSC, FZ Jülich, 52425, Jülich, Germany

    P. Grassberger

  4. Department of Physics and Astronomy, Seoul National University, Seoul, 151-747, Korea

    B. Kahng

  5. Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093, Zurich, Switzerland

    K.J. Schrenk

  6. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK

    K.J. Schrenk

  7. Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, 48109-2136, USA

    R.M. Ziff

Authors
  1. N. Araújo
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  2. P. Grassberger
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  3. B. Kahng
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  4. K.J. Schrenk
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  5. R.M. Ziff
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Corresponding authors

Correspondence to N. Araújo, P. Grassberger, B. Kahng, K.J. Schrenk or R.M. Ziff.

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Araújo, N., Grassberger, P., Kahng, B. et al. Recent advances and open challenges in percolation. Eur. Phys. J. Spec. Top. 223, 2307–2321 (2014). https://doi.org/10.1140/epjst/e2014-02266-y

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  • DOI: https://doi.org/10.1140/epjst/e2014-02266-y

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