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.
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}
}