English

Recent advances and open challenges in percolation

Statistical Mechanics 2014-10-28 v1

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.

Keywords

Cite

@article{arxiv.1404.5325,
  title  = {Recent advances and open challenges in percolation},
  author = {N. A. M. Araújo and P. Grassberger and B. Kahng and K. J. Schrenk and R. M. Ziff},
  journal= {arXiv preprint arXiv:1404.5325},
  year   = {2014}
}
R2 v1 2026-06-22T03:55:13.780Z