# 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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