Topological estimation of percolation thresholds

@article{Neher2007TopologicalEO,
  title={Topological estimation of percolation thresholds},
  author={Richard A. Neher and Klaus Mecke and Herbert Wagner},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2007},
  volume={2008},
  pages={P01011}
}
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two-dimensional lattice graphs, we use the universal scaling form of the cluster size distributions to derive a relation between the mean Euler characteristic of the critical percolation patterns and the threshold density pc. From this relation, we… 

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