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Abstract: Global physical properties of random media change qualitatively at apercolation threshold, where isolated clusters merge to form one infiniteconnected component. The precise knowledge of percolation thresholds is thus ofparamount importance. For two dimensional lattice graphs, we use the universalscaling form of the cluster size distributions to derive a relation between themean Euler characteristic of the critical percolation patterns and thethreshold density $p c$. From this relation, we deduce a simple rule toestimate $p c$, which is remarkably accurate. We present some evidence thatsimilar relations might hold for continuum percolation and percolation inhigher dimensions.



Author: Richard A. Neher, Klaus Mecke, Herbert Wagner

Source: https://arxiv.org/



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